群论导论(第4版)(英文版)

群论导论(第4版)(英文版)
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作者: [美]
出版社: 世界图书出版公司
2009-08
版次: 1
ISBN: 9787510004988
定价: 65.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 513页
正文语种: 英语
分类: 自然科学
  • 《群论导论(第4版)(英文版)》介绍了:GroupTheoryisavastsubjectand,inthisIntroduction(aswellasintheearliereditions),Ihavetriedtoselectimportantandrepresentativetheoremsandtoorganizetheminacoherentway.Proofsmustbeclear,andexamplesshouldillustratetheoremsandalsoexplainthepresenceofrestrictivehypo-theses.!alsobelievethatsomehistoryshouldbegivensothatonecanunderstandtheoriginofproblemsandthecontextinwhichthesubjectdeveloped.Justaseachoftheearliereditionsdiffersfromthepreviousoneinasignifi-cantway,thepresent(fourth)editionisgenuinelydifferentfromthethird.Indeed,thisisalreadyapparentintheTableofContents.Thebooknowbeginswiththeuniquefactorizationofpermutationsintodisjointcyclesandtheparityofpermutations;onlythenistheideaofgroupintroduced.ThisisconsistentwiththehistoryofGroupTheory,forthesefirstresultsonpermu-tationscanbefoundinan1815paperbyCauchy,whereasgroupsofpermu-tationswerenotintroduceduntil1831(byGalois)Butevenifhistory PrefacetotheFourthEdition
    FromPrefacetotheThirdEdition
    TotheReader
    CHAPTER1GroupsandHomomorphisms
    Permutations
    Cycles
    FactorizationintoDisjointCycles
    EvenandOddPermutations
    Semigroups
    Groups
    Homomorphisms

    CHAPTER2TheIsomorphismTheorems
    Subgroups
    LagrangesTheorem
    CycicGroups
    NormalSubgroups
    QuotientGroups
    TheIsomorphismTheorems
    CorrespondenceTheorem
    DirectProducts

    CHAPTER3SymmetricGroupsandG-Sets
    Conjugates
    SymmetricGroups
    TheSimplicityofA.
    SomeRepresentationTheorems
    G-Sets
    CountingOrbits
    SomeGeometry

    CHAPTER4TheSylowTheorems
    p-Groups
    TheSylowTheorems
    GroupsofSmallOrder

    CHAPTER5NormalSeries
    SomeGaloisTheory
    TheJordan-Ho1derTheorem
    SolvableGroups
    TwoTheoremsofP.Hall
    CentralSeriesandNilpotentGroups
    p-Groups

    CHAPTER6FiniteDirectProducts
    TheBasisTheorem
    TheFundamentalTheoremofFiniteAbelianGroups
    CanonicalForms;Existence
    CanonicalForms;Uniqueness
    TheKrulI-SchmidtTheorem
    OperatorGroups

    CHAPTER7ExtensionsandCohomology
    TheExtensionProblem
    AutomorphismGroups
    SemidirectProducts
    WreathProducts
    FactorSets
    TheoremsofSchur-ZassenhausandGaschiJtz
    TransferandBurnsidesTheorem
    ProjectiveRepresentationsandtheSchurMultiplier
    Derivations

    CHAPTER8
    SomeSimpleLinearGroups
    FiniteFields
    TheGeneralLinearGroup
    PSL(2,K)
    PSL(m,K)
    ClassicalGroups

    CHAPTER9
    PermutationsandtheMathieuGroups
    MultipleTransitivity
    PrimitiveG-Sets
    SimplicityCriteria
    AtlineGeometry
    ProjeetiveGeometry
    Sharply3-TransitiveGroups
    MathieuGroups
    SteinerSystems

    CHAPTER10
    AbelianGroups
    Basics
    FreeAbelianGroups
    FinitelyGeneratedAbelianGroups
    DivisibleandReducedGroups
    TorsionGroups
    Subgroupsof
    CharacterGroups

    CHAPTER11
    FreeGroupsandFreeProducts
    GeneratorsandRelations
    SemigroupInterlude
    CosetEnumeration
    PresentationsandtheSchurMultiplier
    FundamentalGroupsofComplexes
    TietzesTheorem
    CoveringComplexes
    TheNielsenSchreierTheorem
    FreeProducts
    TheKuroshTheorem
    ThevanKampenTheorem
    Amalgams
    HNNExtensions

    CHAPTER12
    TheWordProblem
    Introduction
    TuringMachines
    TheMarkov-PostTheorem
    TheNovikov-Boone-BrittonTheorem:SufficiencyofBoones
    Lemma
    CancellationDiagrams
    TheNovikov-Boone-BrittonTheorem:NecessityofBoones
    Lemma
    TheHigmanImbeddingTheorem
    SomeApplications
    Epilogue
    APPENDIXI
    SomeMajorAlgebraicSystems
    APPENDIXII
    EquivalenceRelationsandEquivalenceClasses
    APPENDIXIll
    Functions
    APPENDIXIV
    ZornsLemma
    APPENDIXV
    Countability
    APPENDIXVI
    CommutativeRings
    Bibliography
    Notation
    Index
  • 内容简介:
    《群论导论(第4版)(英文版)》介绍了:GroupTheoryisavastsubjectand,inthisIntroduction(aswellasintheearliereditions),Ihavetriedtoselectimportantandrepresentativetheoremsandtoorganizetheminacoherentway.Proofsmustbeclear,andexamplesshouldillustratetheoremsandalsoexplainthepresenceofrestrictivehypo-theses.!alsobelievethatsomehistoryshouldbegivensothatonecanunderstandtheoriginofproblemsandthecontextinwhichthesubjectdeveloped.Justaseachoftheearliereditionsdiffersfromthepreviousoneinasignifi-cantway,thepresent(fourth)editionisgenuinelydifferentfromthethird.Indeed,thisisalreadyapparentintheTableofContents.Thebooknowbeginswiththeuniquefactorizationofpermutationsintodisjointcyclesandtheparityofpermutations;onlythenistheideaofgroupintroduced.ThisisconsistentwiththehistoryofGroupTheory,forthesefirstresultsonpermu-tationscanbefoundinan1815paperbyCauchy,whereasgroupsofpermu-tationswerenotintroduceduntil1831(byGalois)Butevenifhistory
  • 目录:
    PrefacetotheFourthEdition
    FromPrefacetotheThirdEdition
    TotheReader
    CHAPTER1GroupsandHomomorphisms
    Permutations
    Cycles
    FactorizationintoDisjointCycles
    EvenandOddPermutations
    Semigroups
    Groups
    Homomorphisms

    CHAPTER2TheIsomorphismTheorems
    Subgroups
    LagrangesTheorem
    CycicGroups
    NormalSubgroups
    QuotientGroups
    TheIsomorphismTheorems
    CorrespondenceTheorem
    DirectProducts

    CHAPTER3SymmetricGroupsandG-Sets
    Conjugates
    SymmetricGroups
    TheSimplicityofA.
    SomeRepresentationTheorems
    G-Sets
    CountingOrbits
    SomeGeometry

    CHAPTER4TheSylowTheorems
    p-Groups
    TheSylowTheorems
    GroupsofSmallOrder

    CHAPTER5NormalSeries
    SomeGaloisTheory
    TheJordan-Ho1derTheorem
    SolvableGroups
    TwoTheoremsofP.Hall
    CentralSeriesandNilpotentGroups
    p-Groups

    CHAPTER6FiniteDirectProducts
    TheBasisTheorem
    TheFundamentalTheoremofFiniteAbelianGroups
    CanonicalForms;Existence
    CanonicalForms;Uniqueness
    TheKrulI-SchmidtTheorem
    OperatorGroups

    CHAPTER7ExtensionsandCohomology
    TheExtensionProblem
    AutomorphismGroups
    SemidirectProducts
    WreathProducts
    FactorSets
    TheoremsofSchur-ZassenhausandGaschiJtz
    TransferandBurnsidesTheorem
    ProjectiveRepresentationsandtheSchurMultiplier
    Derivations

    CHAPTER8
    SomeSimpleLinearGroups
    FiniteFields
    TheGeneralLinearGroup
    PSL(2,K)
    PSL(m,K)
    ClassicalGroups

    CHAPTER9
    PermutationsandtheMathieuGroups
    MultipleTransitivity
    PrimitiveG-Sets
    SimplicityCriteria
    AtlineGeometry
    ProjeetiveGeometry
    Sharply3-TransitiveGroups
    MathieuGroups
    SteinerSystems

    CHAPTER10
    AbelianGroups
    Basics
    FreeAbelianGroups
    FinitelyGeneratedAbelianGroups
    DivisibleandReducedGroups
    TorsionGroups
    Subgroupsof
    CharacterGroups

    CHAPTER11
    FreeGroupsandFreeProducts
    GeneratorsandRelations
    SemigroupInterlude
    CosetEnumeration
    PresentationsandtheSchurMultiplier
    FundamentalGroupsofComplexes
    TietzesTheorem
    CoveringComplexes
    TheNielsenSchreierTheorem
    FreeProducts
    TheKuroshTheorem
    ThevanKampenTheorem
    Amalgams
    HNNExtensions

    CHAPTER12
    TheWordProblem
    Introduction
    TuringMachines
    TheMarkov-PostTheorem
    TheNovikov-Boone-BrittonTheorem:SufficiencyofBoones
    Lemma
    CancellationDiagrams
    TheNovikov-Boone-BrittonTheorem:NecessityofBoones
    Lemma
    TheHigmanImbeddingTheorem
    SomeApplications
    Epilogue
    APPENDIXI
    SomeMajorAlgebraicSystems
    APPENDIXII
    EquivalenceRelationsandEquivalenceClasses
    APPENDIXIll
    Functions
    APPENDIXIV
    ZornsLemma
    APPENDIXV
    Countability
    APPENDIXVI
    CommutativeRings
    Bibliography
    Notation
    Index
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