\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Preface}}{23}{chapter.1}
\contentsline {section}{\numberline {1.1}\leavevmode {\color {Chapter }The \textsf {GAP} System}}{23}{section.1.1}
\contentsline {section}{\numberline {1.2}\leavevmode {\color {Chapter }Authors and Maintainers}}{25}{section.1.2}
\contentsline {section}{\numberline {1.3}\leavevmode {\color {Chapter }Acknowledgements}}{25}{section.1.3}
\contentsline {section}{\numberline {1.4}\leavevmode {\color {Chapter }Copyright and License}}{26}{section.1.4}
\contentsline {section}{\numberline {1.5}\leavevmode {\color {Chapter }Further Information about \textsf {GAP}}}{27}{section.1.5}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }The Help System}}{28}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter }Invoking the Help}}{28}{section.2.1}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter }Browsing through the Sections}}{28}{section.2.2}
\contentsline {section}{\numberline {2.3}\leavevmode {\color {Chapter }Changing the Help Viewer}}{29}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}\leavevmode {\color {Chapter }SetHelpViewer}}{30}{subsection.2.3.1}
\contentsline {section}{\numberline {2.4}\leavevmode {\color {Chapter }The Pager Command}}{31}{section.2.4}
\contentsline {subsection}{\numberline {2.4.1}\leavevmode {\color {Chapter }Pager}}{31}{subsection.2.4.1}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Running GAP}}{33}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Command Line Options}}{33}{section.3.1}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }The gap.ini and gaprc files}}{38}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }The gap.ini file}}{38}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}\leavevmode {\color {Chapter }The gaprc file}}{39}{subsection.3.2.2}
\contentsline {subsection}{\numberline {3.2.3}\leavevmode {\color {Chapter }Configuring User preferences}}{39}{subsection.3.2.3}
\contentsline {subsection}{\numberline {3.2.4}\leavevmode {\color {Chapter }DeclareUserPreference}}{40}{subsection.3.2.4}
\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter }Saving and Loading a Workspace}}{41}{section.3.3}
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\contentsline {section}{\numberline {3.4}\leavevmode {\color {Chapter }Testing for the System Architecture}}{42}{section.3.4}
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\contentsline {section}{\numberline {3.6}\leavevmode {\color {Chapter }Coloring the Prompt and Input}}{43}{section.3.6}
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\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }The Programming Language}}{45}{chapter.4}
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\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter }Lexical Structure}}{46}{section.4.2}
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\contentsline {section}{\numberline {4.9}\leavevmode {\color {Chapter }More About Global Variables}}{51}{section.4.9}
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\contentsline {section}{\numberline {4.16}\leavevmode {\color {Chapter }Procedure Calls}}{60}{section.4.16}
\contentsline {section}{\numberline {4.17}\leavevmode {\color {Chapter }If}}{60}{section.4.17}
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\contentsline {subsection}{\numberline {6.9.4}\leavevmode {\color {Chapter }Writing your own command line editing functions}}{97}{subsection.6.9.4}
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\contentsline {section}{\numberline {6.11}\leavevmode {\color {Chapter }Editor Support}}{99}{section.6.11}
\contentsline {section}{\numberline {6.12}\leavevmode {\color {Chapter }Changing the Screen Size}}{100}{section.6.12}
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\contentsline {section}{\numberline {39.24}\leavevmode {\color {Chapter }Schur Covers and Multipliers}}{549}{section.39.24}
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\contentsline {chapter}{\numberline {41}\leavevmode {\color {Chapter }Group Actions}}{571}{chapter.41}
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\contentsline {chapter}{\numberline {42}\leavevmode {\color {Chapter }Permutations}}{594}{chapter.42}
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\contentsline {chapter}{\numberline {45}\leavevmode {\color {Chapter }Polycyclic Groups}}{628}{chapter.45}
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\contentsline {section}{\numberline {45.2}\leavevmode {\color {Chapter }Computing a Pcgs}}{629}{section.45.2}
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\contentsline {section}{\numberline {45.3}\leavevmode {\color {Chapter }Defining a Pcgs Yourself}}{630}{section.45.3}
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\contentsline {section}{\numberline {45.4}\leavevmode {\color {Chapter }Elementary Operations for a Pcgs}}{630}{section.45.4}
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\contentsline {subsection}{\numberline {45.4.2}\leavevmode {\color {Chapter }IsFiniteOrdersPcgs}}{630}{subsection.45.4.2}
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\contentsline {section}{\numberline {45.10}\leavevmode {\color {Chapter }Factor Groups of Polycyclic Groups in their Own Representation}}{639}{section.45.10}
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\contentsline {section}{\numberline {45.15}\leavevmode {\color {Chapter }Orbit Stabilizer Methods for Polycyclic Groups}}{649}{section.45.15}
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\contentsline {chapter}{\numberline {46}\leavevmode {\color {Chapter }Pc Groups}}{651}{chapter.46}
\contentsline {section}{\numberline {46.1}\leavevmode {\color {Chapter }The family pcgs}}{652}{section.46.1}
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\contentsline {subsection}{\numberline {46.2.2}\leavevmode {\color {Chapter }Arithmetic operations for elements of pc groups}}{653}{subsection.46.2.2}
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\contentsline {section}{\numberline {46.4}\leavevmode {\color {Chapter }Constructing Pc Groups}}{654}{section.46.4}
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\contentsline {chapter}{\numberline {48}\leavevmode {\color {Chapter }Presentations and Tietze Transformations}}{690}{chapter.48}
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\contentsline {subsection}{\numberline {50.12.6}\leavevmode {\color {Chapter }IsomorphismPermGroupImfGroup}}{761}{subsection.50.12.6}
\contentsline {chapter}{\numberline {51}\leavevmode {\color {Chapter }Semigroups and Monoids}}{762}{chapter.51}
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\contentsline {subsection}{\numberline {51.3.2}\leavevmode {\color {Chapter }InverseMonoid}}{768}{subsection.51.3.2}
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\contentsline {subsection}{\numberline {51.3.4}\leavevmode {\color {Chapter }GeneratorsOfInverseMonoid}}{769}{subsection.51.3.4}
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\contentsline {section}{\numberline {51.9}\leavevmode {\color {Chapter }Rees Matrix Semigroups}}{776}{section.51.9}
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\contentsline {chapter}{\numberline {52}\leavevmode {\color {Chapter }Finitely Presented Semigroups and Monoids}}{784}{chapter.52}
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\contentsline {chapter}{\numberline {53}\leavevmode {\color {Chapter }Transformations}}{794}{chapter.53}
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\contentsline {chapter}{\numberline {55}\leavevmode {\color {Chapter }Additive Magmas}}{842}{chapter.55}
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\contentsline {chapter}{\numberline {63}\leavevmode {\color {Chapter }Finitely Presented Algebras}}{955}{chapter.63}
\contentsline {chapter}{\numberline {64}\leavevmode {\color {Chapter }Lie Algebras}}{956}{chapter.64}
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\contentsline {subsection}{\numberline {71.10.11}\leavevmode {\color {Chapter }ClassPositionsOfPCore}}{1090}{subsection.71.10.11}
\contentsline {subsection}{\numberline {71.10.12}\leavevmode {\color {Chapter }ClassPositionsOfNormalClosure}}{1090}{subsection.71.10.12}
\contentsline {section}{\numberline {71.11}\leavevmode {\color {Chapter }Operations Concerning Blocks}}{1091}{section.71.11}
\contentsline {subsection}{\numberline {71.11.1}\leavevmode {\color {Chapter }PrimeBlocks}}{1091}{subsection.71.11.1}
\contentsline {subsection}{\numberline {71.11.2}\leavevmode {\color {Chapter }SameBlock}}{1092}{subsection.71.11.2}
\contentsline {subsection}{\numberline {71.11.3}\leavevmode {\color {Chapter }BlocksInfo}}{1092}{subsection.71.11.3}
\contentsline {subsection}{\numberline {71.11.4}\leavevmode {\color {Chapter }DecompositionMatrix}}{1093}{subsection.71.11.4}
\contentsline {subsection}{\numberline {71.11.5}\leavevmode {\color {Chapter }LaTeXStringDecompositionMatrix}}{1093}{subsection.71.11.5}
\contentsline {section}{\numberline {71.12}\leavevmode {\color {Chapter }Other Operations for Character Tables}}{1094}{section.71.12}
\contentsline {subsection}{\numberline {71.12.1}\leavevmode {\color {Chapter }Index (for two character tables)}}{1095}{subsection.71.12.1}
\contentsline {subsection}{\numberline {71.12.2}\leavevmode {\color {Chapter }IsInternallyConsistent (for character tables)}}{1095}{subsection.71.12.2}
\contentsline {subsection}{\numberline {71.12.3}\leavevmode {\color {Chapter }IsPSolvableCharacterTable}}{1095}{subsection.71.12.3}
\contentsline {subsection}{\numberline {71.12.4}\leavevmode {\color {Chapter }IsClassFusionOfNormalSubgroup}}{1096}{subsection.71.12.4}
\contentsline {subsection}{\numberline {71.12.5}\leavevmode {\color {Chapter }Indicator}}{1096}{subsection.71.12.5}
\contentsline {subsection}{\numberline {71.12.6}\leavevmode {\color {Chapter }NrPolyhedralSubgroups}}{1096}{subsection.71.12.6}
\contentsline {subsection}{\numberline {71.12.7}\leavevmode {\color {Chapter }ClassMultiplicationCoefficient (for character tables)}}{1097}{subsection.71.12.7}
\contentsline {subsection}{\numberline {71.12.8}\leavevmode {\color {Chapter }ClassStructureCharTable}}{1097}{subsection.71.12.8}
\contentsline {subsection}{\numberline {71.12.9}\leavevmode {\color {Chapter }MatClassMultCoeffsCharTable}}{1098}{subsection.71.12.9}
\contentsline {section}{\numberline {71.13}\leavevmode {\color {Chapter }Printing Character Tables}}{1098}{section.71.13}
\contentsline {subsection}{\numberline {71.13.1}\leavevmode {\color {Chapter }ViewObj (for a character table)}}{1098}{subsection.71.13.1}
\contentsline {subsection}{\numberline {71.13.2}\leavevmode {\color {Chapter }PrintObj (for a character table)}}{1098}{subsection.71.13.2}
\contentsline {subsection}{\numberline {71.13.3}\leavevmode {\color {Chapter }Display (for a character table)}}{1098}{subsection.71.13.3}
\contentsline {subsection}{\numberline {71.13.4}\leavevmode {\color {Chapter }DisplayOptions}}{1100}{subsection.71.13.4}
\contentsline {subsection}{\numberline {71.13.5}\leavevmode {\color {Chapter }PrintCharacterTable}}{1101}{subsection.71.13.5}
\contentsline {section}{\numberline {71.14}\leavevmode {\color {Chapter }Computing the Irreducible Characters of a Group}}{1102}{section.71.14}
\contentsline {subsection}{\numberline {71.14.1}\leavevmode {\color {Chapter }IrrDixonSchneider}}{1103}{subsection.71.14.1}
\contentsline {subsection}{\numberline {71.14.2}\leavevmode {\color {Chapter }IrrConlon}}{1103}{subsection.71.14.2}
\contentsline {subsection}{\numberline {71.14.3}\leavevmode {\color {Chapter }IrrBaumClausen}}{1103}{subsection.71.14.3}
\contentsline {subsection}{\numberline {71.14.4}\leavevmode {\color {Chapter }IrreducibleRepresentations}}{1104}{subsection.71.14.4}
\contentsline {subsection}{\numberline {71.14.5}\leavevmode {\color {Chapter }IrreducibleRepresentationsDixon}}{1105}{subsection.71.14.5}
\contentsline {section}{\numberline {71.15}\leavevmode {\color {Chapter }Representations Given by Modules}}{1105}{section.71.15}
\contentsline {subsection}{\numberline {71.15.1}\leavevmode {\color {Chapter }IrreducibleModules}}{1105}{subsection.71.15.1}
\contentsline {subsection}{\numberline {71.15.2}\leavevmode {\color {Chapter }AbsolutelyIrreducibleModules}}{1105}{subsection.71.15.2}
\contentsline {subsection}{\numberline {71.15.3}\leavevmode {\color {Chapter }RegularModule}}{1106}{subsection.71.15.3}
\contentsline {section}{\numberline {71.16}\leavevmode {\color {Chapter }The Dixon-Schneider Algorithm}}{1106}{section.71.16}
\contentsline {section}{\numberline {71.17}\leavevmode {\color {Chapter }Advanced Methods for Dixon-Schneider Calculations}}{1106}{section.71.17}
\contentsline {subsection}{\numberline {71.17.1}\leavevmode {\color {Chapter }DixonRecord}}{1107}{subsection.71.17.1}
\contentsline {subsection}{\numberline {71.17.2}\leavevmode {\color {Chapter }DixonInit}}{1107}{subsection.71.17.2}
\contentsline {subsection}{\numberline {71.17.3}\leavevmode {\color {Chapter }DixontinI}}{1107}{subsection.71.17.3}
\contentsline {subsection}{\numberline {71.17.4}\leavevmode {\color {Chapter }DixonSplit}}{1107}{subsection.71.17.4}
\contentsline {subsection}{\numberline {71.17.5}\leavevmode {\color {Chapter }BestSplittingMatrix}}{1107}{subsection.71.17.5}
\contentsline {subsection}{\numberline {71.17.6}\leavevmode {\color {Chapter }DxIncludeIrreducibles}}{1108}{subsection.71.17.6}
\contentsline {subsection}{\numberline {71.17.7}\leavevmode {\color {Chapter }SplitCharacters}}{1108}{subsection.71.17.7}
\contentsline {subsection}{\numberline {71.17.8}\leavevmode {\color {Chapter }IsDxLargeGroup}}{1108}{subsection.71.17.8}
\contentsline {section}{\numberline {71.18}\leavevmode {\color {Chapter }Components of a Dixon Record}}{1108}{section.71.18}
\contentsline {section}{\numberline {71.19}\leavevmode {\color {Chapter }An Example of Advanced Dixon-Schneider Calculations}}{1109}{section.71.19}
\contentsline {section}{\numberline {71.20}\leavevmode {\color {Chapter }Constructing Character Tables from Others}}{1111}{section.71.20}
\contentsline {subsection}{\numberline {71.20.1}\leavevmode {\color {Chapter }CharacterTableDirectProduct}}{1111}{subsection.71.20.1}
\contentsline {subsection}{\numberline {71.20.2}\leavevmode {\color {Chapter }FactorsOfDirectProduct}}{1112}{subsection.71.20.2}
\contentsline {subsection}{\numberline {71.20.3}\leavevmode {\color {Chapter }CharacterTableFactorGroup}}{1112}{subsection.71.20.3}
\contentsline {subsection}{\numberline {71.20.4}\leavevmode {\color {Chapter }CharacterTableIsoclinic}}{1113}{subsection.71.20.4}
\contentsline {subsection}{\numberline {71.20.5}\leavevmode {\color {Chapter }CharacterTableWreathSymmetric}}{1113}{subsection.71.20.5}
\contentsline {section}{\numberline {71.21}\leavevmode {\color {Chapter }Sorted Character Tables}}{1114}{section.71.21}
\contentsline {subsection}{\numberline {71.21.1}\leavevmode {\color {Chapter }CharacterTableWithSortedCharacters}}{1114}{subsection.71.21.1}
\contentsline {subsection}{\numberline {71.21.2}\leavevmode {\color {Chapter }SortedCharacters}}{1115}{subsection.71.21.2}
\contentsline {subsection}{\numberline {71.21.3}\leavevmode {\color {Chapter }CharacterTableWithSortedClasses}}{1115}{subsection.71.21.3}
\contentsline {subsection}{\numberline {71.21.4}\leavevmode {\color {Chapter }SortedCharacterTable (w.r.t. a normal subgroup)}}{1115}{subsection.71.21.4}
\contentsline {subsection}{\numberline {71.21.5}\leavevmode {\color {Chapter }ClassPermutation}}{1116}{subsection.71.21.5}
\contentsline {section}{\numberline {71.22}\leavevmode {\color {Chapter }Automorphisms and Equivalence of Character Tables}}{1117}{section.71.22}
\contentsline {subsection}{\numberline {71.22.1}\leavevmode {\color {Chapter }MatrixAutomorphisms}}{1117}{subsection.71.22.1}
\contentsline {subsection}{\numberline {71.22.2}\leavevmode {\color {Chapter }TableAutomorphisms}}{1117}{subsection.71.22.2}
\contentsline {subsection}{\numberline {71.22.3}\leavevmode {\color {Chapter }TransformingPermutations}}{1118}{subsection.71.22.3}
\contentsline {subsection}{\numberline {71.22.4}\leavevmode {\color {Chapter }TransformingPermutationsCharacterTables}}{1118}{subsection.71.22.4}
\contentsline {subsection}{\numberline {71.22.5}\leavevmode {\color {Chapter }FamiliesOfRows}}{1119}{subsection.71.22.5}
\contentsline {section}{\numberline {71.23}\leavevmode {\color {Chapter }Storing Normal Subgroup Information}}{1119}{section.71.23}
\contentsline {subsection}{\numberline {71.23.1}\leavevmode {\color {Chapter }NormalSubgroupClassesInfo}}{1119}{subsection.71.23.1}
\contentsline {subsection}{\numberline {71.23.2}\leavevmode {\color {Chapter }ClassPositionsOfNormalSubgroup}}{1120}{subsection.71.23.2}
\contentsline {subsection}{\numberline {71.23.3}\leavevmode {\color {Chapter }NormalSubgroupClasses}}{1120}{subsection.71.23.3}
\contentsline {subsection}{\numberline {71.23.4}\leavevmode {\color {Chapter }FactorGroupNormalSubgroupClasses}}{1120}{subsection.71.23.4}
\contentsline {chapter}{\numberline {72}\leavevmode {\color {Chapter }Class Functions}}{1122}{chapter.72}
\contentsline {section}{\numberline {72.1}\leavevmode {\color {Chapter }Why Class Functions?}}{1122}{section.72.1}
\contentsline {subsection}{\numberline {72.1.1}\leavevmode {\color {Chapter }IsClassFunction}}{1124}{subsection.72.1.1}
\contentsline {section}{\numberline {72.2}\leavevmode {\color {Chapter }Basic Operations for Class Functions}}{1125}{section.72.2}
\contentsline {subsection}{\numberline {72.2.1}\leavevmode {\color {Chapter }UnderlyingCharacterTable}}{1125}{subsection.72.2.1}
\contentsline {subsection}{\numberline {72.2.2}\leavevmode {\color {Chapter }ValuesOfClassFunction}}{1125}{subsection.72.2.2}
\contentsline {section}{\numberline {72.3}\leavevmode {\color {Chapter }Comparison of Class Functions}}{1126}{section.72.3}
\contentsline {section}{\numberline {72.4}\leavevmode {\color {Chapter }Arithmetic Operations for Class Functions}}{1126}{section.72.4}
\contentsline {subsection}{\numberline {72.4.1}\leavevmode {\color {Chapter }Characteristic (for a class function)}}{1129}{subsection.72.4.1}
\contentsline {subsection}{\numberline {72.4.2}\leavevmode {\color {Chapter }ComplexConjugate (for a class function)}}{1129}{subsection.72.4.2}
\contentsline {subsection}{\numberline {72.4.3}\leavevmode {\color {Chapter }Order (for a class function)}}{1130}{subsection.72.4.3}
\contentsline {section}{\numberline {72.5}\leavevmode {\color {Chapter }Printing Class Functions}}{1130}{section.72.5}
\contentsline {subsection}{\numberline {72.5.1}\leavevmode {\color {Chapter }ViewObj (for class functions)}}{1130}{subsection.72.5.1}
\contentsline {subsection}{\numberline {72.5.2}\leavevmode {\color {Chapter }PrintObj (for class functions)}}{1130}{subsection.72.5.2}
\contentsline {subsection}{\numberline {72.5.3}\leavevmode {\color {Chapter }Display (for class functions)}}{1130}{subsection.72.5.3}
\contentsline {section}{\numberline {72.6}\leavevmode {\color {Chapter }Creating Class Functions from Values Lists}}{1131}{section.72.6}
\contentsline {subsection}{\numberline {72.6.1}\leavevmode {\color {Chapter }ClassFunction (for a character table and a list)}}{1131}{subsection.72.6.1}
\contentsline {subsection}{\numberline {72.6.2}\leavevmode {\color {Chapter }VirtualCharacter (for a character table and a list)}}{1131}{subsection.72.6.2}
\contentsline {subsection}{\numberline {72.6.3}\leavevmode {\color {Chapter }Character (for a character table and a list)}}{1131}{subsection.72.6.3}
\contentsline {subsection}{\numberline {72.6.4}\leavevmode {\color {Chapter }ClassFunctionSameType}}{1132}{subsection.72.6.4}
\contentsline {section}{\numberline {72.7}\leavevmode {\color {Chapter }Creating Class Functions using Groups}}{1132}{section.72.7}
\contentsline {subsection}{\numberline {72.7.1}\leavevmode {\color {Chapter }TrivialCharacter}}{1132}{subsection.72.7.1}
\contentsline {subsection}{\numberline {72.7.2}\leavevmode {\color {Chapter }NaturalCharacter (for a group)}}{1132}{subsection.72.7.2}
\contentsline {subsection}{\numberline {72.7.3}\leavevmode {\color {Chapter }PermutationCharacter}}{1133}{subsection.72.7.3}
\contentsline {section}{\numberline {72.8}\leavevmode {\color {Chapter }Operations for Class Functions}}{1133}{section.72.8}
\contentsline {subsection}{\numberline {72.8.1}\leavevmode {\color {Chapter }IsCharacter}}{1134}{subsection.72.8.1}
\contentsline {subsection}{\numberline {72.8.2}\leavevmode {\color {Chapter }IsVirtualCharacter}}{1134}{subsection.72.8.2}
\contentsline {subsection}{\numberline {72.8.3}\leavevmode {\color {Chapter }IsIrreducibleCharacter}}{1134}{subsection.72.8.3}
\contentsline {subsection}{\numberline {72.8.4}\leavevmode {\color {Chapter }DegreeOfCharacter}}{1134}{subsection.72.8.4}
\contentsline {subsection}{\numberline {72.8.5}\leavevmode {\color {Chapter }ScalarProduct (for characters)}}{1135}{subsection.72.8.5}
\contentsline {subsection}{\numberline {72.8.6}\leavevmode {\color {Chapter }MatScalarProducts}}{1135}{subsection.72.8.6}
\contentsline {subsection}{\numberline {72.8.7}\leavevmode {\color {Chapter }Norm (for a class function)}}{1135}{subsection.72.8.7}
\contentsline {subsection}{\numberline {72.8.8}\leavevmode {\color {Chapter }ConstituentsOfCharacter}}{1136}{subsection.72.8.8}
\contentsline {subsection}{\numberline {72.8.9}\leavevmode {\color {Chapter }KernelOfCharacter}}{1136}{subsection.72.8.9}
\contentsline {subsection}{\numberline {72.8.10}\leavevmode {\color {Chapter }ClassPositionsOfKernel}}{1136}{subsection.72.8.10}
\contentsline {subsection}{\numberline {72.8.11}\leavevmode {\color {Chapter }CentreOfCharacter}}{1137}{subsection.72.8.11}
\contentsline {subsection}{\numberline {72.8.12}\leavevmode {\color {Chapter }ClassPositionsOfCentre (for a character)}}{1137}{subsection.72.8.12}
\contentsline {subsection}{\numberline {72.8.13}\leavevmode {\color {Chapter }InertiaSubgroup}}{1137}{subsection.72.8.13}
\contentsline {subsection}{\numberline {72.8.14}\leavevmode {\color {Chapter }CycleStructureClass}}{1138}{subsection.72.8.14}
\contentsline {subsection}{\numberline {72.8.15}\leavevmode {\color {Chapter }IsTransitive (for a character)}}{1138}{subsection.72.8.15}
\contentsline {subsection}{\numberline {72.8.16}\leavevmode {\color {Chapter }Transitivity (for a character)}}{1138}{subsection.72.8.16}
\contentsline {subsection}{\numberline {72.8.17}\leavevmode {\color {Chapter }CentralCharacter}}{1138}{subsection.72.8.17}
\contentsline {subsection}{\numberline {72.8.18}\leavevmode {\color {Chapter }DeterminantOfCharacter}}{1138}{subsection.72.8.18}
\contentsline {subsection}{\numberline {72.8.19}\leavevmode {\color {Chapter }EigenvaluesChar}}{1139}{subsection.72.8.19}
\contentsline {subsection}{\numberline {72.8.20}\leavevmode {\color {Chapter }Tensored}}{1139}{subsection.72.8.20}
\contentsline {section}{\numberline {72.9}\leavevmode {\color {Chapter }Restricted and Induced Class Functions}}{1140}{section.72.9}
\contentsline {subsection}{\numberline {72.9.1}\leavevmode {\color {Chapter }RestrictedClassFunction}}{1140}{subsection.72.9.1}
\contentsline {subsection}{\numberline {72.9.2}\leavevmode {\color {Chapter }RestrictedClassFunctions}}{1140}{subsection.72.9.2}
\contentsline {subsection}{\numberline {72.9.3}\leavevmode {\color {Chapter }InducedClassFunction}}{1141}{subsection.72.9.3}
\contentsline {subsection}{\numberline {72.9.4}\leavevmode {\color {Chapter }InducedClassFunctions}}{1141}{subsection.72.9.4}
\contentsline {subsection}{\numberline {72.9.5}\leavevmode {\color {Chapter }InducedClassFunctionsByFusionMap}}{1141}{subsection.72.9.5}
\contentsline {subsection}{\numberline {72.9.6}\leavevmode {\color {Chapter }InducedCyclic}}{1142}{subsection.72.9.6}
\contentsline {section}{\numberline {72.10}\leavevmode {\color {Chapter }Reducing Virtual Characters}}{1142}{section.72.10}
\contentsline {subsection}{\numberline {72.10.1}\leavevmode {\color {Chapter }ReducedClassFunctions}}{1142}{subsection.72.10.1}
\contentsline {subsection}{\numberline {72.10.2}\leavevmode {\color {Chapter }ReducedCharacters}}{1143}{subsection.72.10.2}
\contentsline {subsection}{\numberline {72.10.3}\leavevmode {\color {Chapter }IrreducibleDifferences}}{1143}{subsection.72.10.3}
\contentsline {subsection}{\numberline {72.10.4}\leavevmode {\color {Chapter }LLL}}{1143}{subsection.72.10.4}
\contentsline {subsection}{\numberline {72.10.5}\leavevmode {\color {Chapter }Extract}}{1144}{subsection.72.10.5}
\contentsline {subsection}{\numberline {72.10.6}\leavevmode {\color {Chapter }OrthogonalEmbeddingsSpecialDimension}}{1145}{subsection.72.10.6}
\contentsline {subsection}{\numberline {72.10.7}\leavevmode {\color {Chapter }Decreased}}{1147}{subsection.72.10.7}
\contentsline {subsection}{\numberline {72.10.8}\leavevmode {\color {Chapter }DnLattice}}{1148}{subsection.72.10.8}
\contentsline {subsection}{\numberline {72.10.9}\leavevmode {\color {Chapter }DnLatticeIterative}}{1149}{subsection.72.10.9}
\contentsline {section}{\numberline {72.11}\leavevmode {\color {Chapter }Symmetrizations of Class Functions}}{1149}{section.72.11}
\contentsline {subsection}{\numberline {72.11.1}\leavevmode {\color {Chapter }Symmetrizations}}{1149}{subsection.72.11.1}
\contentsline {subsection}{\numberline {72.11.2}\leavevmode {\color {Chapter }SymmetricParts}}{1150}{subsection.72.11.2}
\contentsline {subsection}{\numberline {72.11.3}\leavevmode {\color {Chapter }AntiSymmetricParts}}{1150}{subsection.72.11.3}
\contentsline {subsection}{\numberline {72.11.4}\leavevmode {\color {Chapter }OrthogonalComponents}}{1150}{subsection.72.11.4}
\contentsline {subsection}{\numberline {72.11.5}\leavevmode {\color {Chapter }SymplecticComponents}}{1151}{subsection.72.11.5}
\contentsline {section}{\numberline {72.12}\leavevmode {\color {Chapter }Molien Series}}{1152}{section.72.12}
\contentsline {subsection}{\numberline {72.12.1}\leavevmode {\color {Chapter }MolienSeries}}{1152}{subsection.72.12.1}
\contentsline {subsection}{\numberline {72.12.2}\leavevmode {\color {Chapter }MolienSeriesInfo}}{1152}{subsection.72.12.2}
\contentsline {subsection}{\numberline {72.12.3}\leavevmode {\color {Chapter }ValueMolienSeries}}{1153}{subsection.72.12.3}
\contentsline {subsection}{\numberline {72.12.4}\leavevmode {\color {Chapter }MolienSeriesWithGivenDenominator}}{1154}{subsection.72.12.4}
\contentsline {section}{\numberline {72.13}\leavevmode {\color {Chapter }Possible Permutation Characters}}{1154}{section.72.13}
\contentsline {subsection}{\numberline {72.13.1}\leavevmode {\color {Chapter }PermCharInfo}}{1155}{subsection.72.13.1}
\contentsline {subsection}{\numberline {72.13.2}\leavevmode {\color {Chapter }PermCharInfoRelative}}{1156}{subsection.72.13.2}
\contentsline {section}{\numberline {72.14}\leavevmode {\color {Chapter }Computing Possible Permutation Characters}}{1157}{section.72.14}
\contentsline {subsection}{\numberline {72.14.1}\leavevmode {\color {Chapter }PermChars}}{1157}{subsection.72.14.1}
\contentsline {subsection}{\numberline {72.14.2}\leavevmode {\color {Chapter }TestPerm1, ..., TestPerm5}}{1159}{subsection.72.14.2}
\contentsline {subsection}{\numberline {72.14.3}\leavevmode {\color {Chapter }PermBounds}}{1160}{subsection.72.14.3}
\contentsline {subsection}{\numberline {72.14.4}\leavevmode {\color {Chapter }PermComb}}{1160}{subsection.72.14.4}
\contentsline {subsection}{\numberline {72.14.5}\leavevmode {\color {Chapter }Inequalities}}{1161}{subsection.72.14.5}
\contentsline {section}{\numberline {72.15}\leavevmode {\color {Chapter }Operations for Brauer Characters}}{1162}{section.72.15}
\contentsline {subsection}{\numberline {72.15.1}\leavevmode {\color {Chapter }FrobeniusCharacterValue}}{1162}{subsection.72.15.1}
\contentsline {subsection}{\numberline {72.15.2}\leavevmode {\color {Chapter }BrauerCharacterValue}}{1162}{subsection.72.15.2}
\contentsline {subsection}{\numberline {72.15.3}\leavevmode {\color {Chapter }SizeOfFieldOfDefinition}}{1162}{subsection.72.15.3}
\contentsline {subsection}{\numberline {72.15.4}\leavevmode {\color {Chapter }RealizableBrauerCharacters}}{1163}{subsection.72.15.4}
\contentsline {section}{\numberline {72.16}\leavevmode {\color {Chapter }Domains Generated by Class Functions}}{1163}{section.72.16}
\contentsline {chapter}{\numberline {73}\leavevmode {\color {Chapter }Maps Concerning Character Tables}}{1164}{chapter.73}
\contentsline {section}{\numberline {73.1}\leavevmode {\color {Chapter }Power Maps}}{1164}{section.73.1}
\contentsline {subsection}{\numberline {73.1.1}\leavevmode {\color {Chapter }PowerMap}}{1165}{subsection.73.1.1}
\contentsline {subsection}{\numberline {73.1.2}\leavevmode {\color {Chapter }PossiblePowerMaps}}{1166}{subsection.73.1.2}
\contentsline {subsection}{\numberline {73.1.3}\leavevmode {\color {Chapter }ElementOrdersPowerMap}}{1167}{subsection.73.1.3}
\contentsline {subsection}{\numberline {73.1.4}\leavevmode {\color {Chapter }PowerMapByComposition}}{1168}{subsection.73.1.4}
\contentsline {section}{\numberline {73.2}\leavevmode {\color {Chapter }Orbits on Sets of Possible Power Maps}}{1168}{section.73.2}
\contentsline {subsection}{\numberline {73.2.1}\leavevmode {\color {Chapter }OrbitPowerMaps}}{1168}{subsection.73.2.1}
\contentsline {subsection}{\numberline {73.2.2}\leavevmode {\color {Chapter }RepresentativesPowerMaps}}{1168}{subsection.73.2.2}
\contentsline {section}{\numberline {73.3}\leavevmode {\color {Chapter }Class Fusions between Character Tables}}{1169}{section.73.3}
\contentsline {subsection}{\numberline {73.3.1}\leavevmode {\color {Chapter }FusionConjugacyClasses}}{1170}{subsection.73.3.1}
\contentsline {subsection}{\numberline {73.3.2}\leavevmode {\color {Chapter }ComputedClassFusions}}{1171}{subsection.73.3.2}
\contentsline {subsection}{\numberline {73.3.3}\leavevmode {\color {Chapter }GetFusionMap}}{1171}{subsection.73.3.3}
\contentsline {subsection}{\numberline {73.3.4}\leavevmode {\color {Chapter }StoreFusion}}{1172}{subsection.73.3.4}
\contentsline {subsection}{\numberline {73.3.5}\leavevmode {\color {Chapter }NamesOfFusionSources}}{1172}{subsection.73.3.5}
\contentsline {subsection}{\numberline {73.3.6}\leavevmode {\color {Chapter }PossibleClassFusions}}{1173}{subsection.73.3.6}
\contentsline {subsection}{\numberline {73.3.7}\leavevmode {\color {Chapter }ConsiderStructureConstants}}{1174}{subsection.73.3.7}
\contentsline {section}{\numberline {73.4}\leavevmode {\color {Chapter }Orbits on Sets of Possible Class Fusions}}{1175}{section.73.4}
\contentsline {subsection}{\numberline {73.4.1}\leavevmode {\color {Chapter }OrbitFusions}}{1175}{subsection.73.4.1}
\contentsline {subsection}{\numberline {73.4.2}\leavevmode {\color {Chapter }RepresentativesFusions}}{1175}{subsection.73.4.2}
\contentsline {section}{\numberline {73.5}\leavevmode {\color {Chapter }Parametrized Maps}}{1175}{section.73.5}
\contentsline {subsection}{\numberline {73.5.1}\leavevmode {\color {Chapter }CompositionMaps}}{1176}{subsection.73.5.1}
\contentsline {subsection}{\numberline {73.5.2}\leavevmode {\color {Chapter }InverseMap}}{1176}{subsection.73.5.2}
\contentsline {subsection}{\numberline {73.5.3}\leavevmode {\color {Chapter }ProjectionMap}}{1177}{subsection.73.5.3}
\contentsline {subsection}{\numberline {73.5.4}\leavevmode {\color {Chapter }Indirected}}{1177}{subsection.73.5.4}
\contentsline {subsection}{\numberline {73.5.5}\leavevmode {\color {Chapter }Parametrized}}{1177}{subsection.73.5.5}
\contentsline {subsection}{\numberline {73.5.6}\leavevmode {\color {Chapter }ContainedMaps}}{1178}{subsection.73.5.6}
\contentsline {subsection}{\numberline {73.5.7}\leavevmode {\color {Chapter }UpdateMap}}{1178}{subsection.73.5.7}
\contentsline {subsection}{\numberline {73.5.8}\leavevmode {\color {Chapter }MeetMaps}}{1179}{subsection.73.5.8}
\contentsline {subsection}{\numberline {73.5.9}\leavevmode {\color {Chapter }CommutativeDiagram}}{1179}{subsection.73.5.9}
\contentsline {subsection}{\numberline {73.5.10}\leavevmode {\color {Chapter }CheckFixedPoints}}{1180}{subsection.73.5.10}
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\contentsline {section}{\numberline {87.1}\leavevmode {\color {Chapter }Generalized Conjugation Technique}}{1304}{section.87.1}
\contentsline {section}{\numberline {87.2}\leavevmode {\color {Chapter }The General Backtrack Algorithm with Ordered Partitions}}{1305}{section.87.2}
\contentsline {subsection}{\numberline {87.2.1}\leavevmode {\color {Chapter }Internal representation of ordered partitions}}{1305}{subsection.87.2.1}
\contentsline {subsection}{\numberline {87.2.2}\leavevmode {\color {Chapter }Functions for setting up an R-base}}{1306}{subsection.87.2.2}
\contentsline {subsection}{\numberline {87.2.3}\leavevmode {\color {Chapter }Refinement functions for the backtrack search}}{1309}{subsection.87.2.3}
\contentsline {subsection}{\numberline {87.2.4}\leavevmode {\color {Chapter }Functions for meeting ordered partitions}}{1311}{subsection.87.2.4}
\contentsline {subsection}{\numberline {87.2.5}\leavevmode {\color {Chapter }Avoiding multiplication of permutations}}{1312}{subsection.87.2.5}
\contentsline {section}{\numberline {87.3}\leavevmode {\color {Chapter }Stabilizer Chains for Automorphisms Acting on Enumerators}}{1313}{section.87.3}
\contentsline {subsection}{\numberline {87.3.1}\leavevmode {\color {Chapter }An operation domain for automorphisms}}{1313}{subsection.87.3.1}
\contentsline {subsection}{\numberline {87.3.2}\leavevmode {\color {Chapter }Enumerators for cosets of characteristic factors}}{1314}{subsection.87.3.2}
\contentsline {subsection}{\numberline {87.3.3}\leavevmode {\color {Chapter }Making automorphisms act on such enumerators}}{1315}{subsection.87.3.3}
\contentsline {chapter}{References}{1327}{chapter*.3}
\contentsline {chapter}{Index}{1328}{section*.4}
