A Book of Abstract Algebra 1982

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1、ABOOKOFABSTRACTALGEBRACharlesC.PinterProfessorofMathematicsBucknellUniversityMcGraw-HillBookCompanyNewYorkSt.LouisSanFranciscoAucklandBogotaHamburgJohannesburgLondonMadridMexicoMontrealNewDelhiPanamaParisSãoPauloSingaporeSydneyTokyoTorontoThisbookwassetinTimesRo

2、manbySantype-Byrd.TheeditorswereJohnJ.CorriganandJamesS.Amar;theproductionsupervisorwasLeroyA.Young.ThedrawingsweredonebyVIPGraphics.ThecoverwasdesignedbyScottChelius.R.R.Donnelley&SonsCompanywasprinterandbinder.ABOOKOFABSTRACTALGEBRACopyright©1982byMcGraw-Hill,

3、Inc.Allrightsreserved.PrintedintheUnitedStatesofAmerica.ExceptaspermittedundertheUnitedStatesCopyrightActof1976,nopartofthispublicationmaybereproducedordistributedinanyformorbyanymeans,orstoredinadatabaseorretrievalsystem,withoutthepriorwrittenpermissionofthepub

4、lisher.1234567890DODO8987654321ISBN0—07—050130—0LibraryofCongressCataloginginPublicationDataPinter,CharlesC.,dateAbookofabstractalgebra.Includesindex.1.Algebra,Abstract.I.Title.QA162.P56512.0281-8420ISBN0-07-050130-0AACR2TomycolleaguesinBrazil,especiallyNewtonda

5、Costa,AydaArruda,andEliasAlves,aswellastoothers.Inappreciationoftheirloyalandvaluedfriendship.CONTENTS*PrefacexiiiChapter1WhyAbstractAlgebra?HistoryofAlgebra.NewAlgebras.AlgebraicStructures.AxiomsandAxiomaticAlgebra.AbstractioninAlgebra.Chapter2Operations20Opera

6、tionsonaSet.PropertiesofOperations.Chapter3TheDefinitionofGroups26Groups.ExamplesofInfiniteandFiniteGroups.ExamplesofAbelianandNonabelianGroups.GroupTables.Chapter4ElementaryPropertiesofGroups36UniquenessofIdentityandInverses.PropertiesofInverses.DirectProductof

7、Groups.5Subgroups45DefinitionofSubgroup.GeneratorsandDefiningRelations.CayleyDiagrams.CenterofaGroup.*Italicheadingsindicatetopicsdiscussedintheexercisesections.VIIviiiCONTENTSChapter6Functions54Injective,.Surjective,BijectiveFunction.CompositeandInverseofFuncti

8、ons.Chapter7GroupsofPermutations64SymmetricGroups.DihedralGroups.Chapter8PermutationsofaFiniteSet75DecompositionofPermutationsintoCycles.Transpositions.EvenandOddPerm