群论导论（第4版）（英文版）an introduction to the theory of groups

图书标准信息

• 作者 [美]罗曼 著
• 出版社 世界图书出版公司
• 出版时间 2009-08
• 版次 1
• ISBN 9787510004988
• 定价 65.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 513页
• 正文语种 英语

【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