群论教程

　　A group is defin

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Preface
Notation
Chapter1
FundamentalConceptsofGroupTheory
1.1BinaryOperations,Semigroups,andGroups
1.2ExamplesofGroups
1.3SubgroupsandCosets
1.4HomomorphismsandQuotientGroups
1.5EndomorphismsandAutomorphisms
1.6PermutationGroupsandGroupActions
Chapter2
FreeGroupsandPresentations
2.1FreeGroups
2.2PresentationsofGroups
2.3VarietiesofGroups
Chapter3
DecompositionsofaGroup
3.1SeriesandCompositionSeries
3.2SomeSimpleGroups
3.3DirectDecompositions
Chapter4
AbelianGroups
4.1TorsionGroupsandDivisibleGroups
4.2DirectSumsofCyclicandQuasicyclicGroups
4.3PureSubgroupsandp-groups
4.4Torsion-freeGroups
Chapter5
SolubleandNilpotentGroups
5.1AbelianandCentralSeries
5.2NilpotentGroups
5.3GroupsofPrime-PowerOrder
5.4SolubleGroups
Chapter6
FreeGroupsandFreeProducts
6.1FurtherPropertiesofFreeGroups
6.2FreeProductsofGroups
6.3SubgroupsofFreeProducts
6.4GeneralizedFreeProducts
Chapter7
FinitePermutationGroups
7.1MultipleTransitivity
7.2PrimitivePermutationGroups
7.3ClassificationofSharplyk-transitivePermutationGroups
7.4TheMathieuGroups
Chapter8
RepresentationsofGroups
8.1RepresentationsandModules
8.2StructureoftheGroupAlgebra
8.3Characters
8.4TensorProductsandRepresentations
8.5ApplicationstoFiniteGroups
Chapter9
FiniteSolubleGroups
9.1Halln-subgroups
9.2SylowSystemsandSystemNormalizers
9.3p-solubleGroups
9.4SupersolubleGroups
9.5Formations
Chapter10
TheTransferandItsApplications
10.1TheTransferHomomorphism
10.2Griin,sTheorems
10.3Frobenius'Criterionforp-nilpotence
10.4Thompson'sCriterionforp-nilpotence
10.5Fixed-point-freeAutomorphisms
Chapter11
TheTheoryofGroupExtensions
11.1GroupExtensionsandCoveringGroups
11.2HomologyGroupsandCohomologyGroups
11.3TheGruenbergResolution
11.4Group-theoreticInterpretationsofthe(Co)homologyGroups
Chapter12
GeneralizationsofNilpotentandSolubleGroups
12.1LocallyNilpotentGroups
12.2SomeSpecialTypesofLocallyNilpotentGroups
12.3EngelElementsandEngelGroups
12.4ClassesofGroupsDefinedbyGeneralSeries
12.5LocallySolubleGroups
Chapter13
SubnormalSubgroups
13.1JoinsandIntersectionsofSubnormalSubgroups
13.2PermutabilityandSubnormality
13.3TheMinimalConditiononSubnormalSubgroups
13.4GroupsinWhichNormalityIsaTransitiveRelation
13.5AutomorphismTowersandCompleteGroups
Chapter14
FinitenessProperties
14.1FinitelyGeneratedGroupsandFinitelyPresentedGroups
14.2TorsionGroupsandtheBurnsideProblems
14.3LocallyFiniteGroups
14.42-groupswiththeMaximalorMinimalCondition
14.5FinitenessPropertiesofConjugatesandCommutators
Chapter15
InfiniteSolubleGroups
15.1SolubleLinearGroups
15.2SolubleGroupswithFinitenessConditionsonAbelianSubgroups
15.3FinitelyGeneratedSolubleGroupsandtheMaximalConditionon
NormalSubgroups
15.4FinitelyGeneratedSolubleGroupsandResidualFiniteness
15.5FinitelyGeneratedSolubleGroupsandTheirFrattiniSubgroups
Bibliography.
Index