EMS_Algebra_04__Infinite_Groups__Linear_Groups .pdf

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1、AsftA.I.KostrikinI.R.Shafarevich(Eds.)AlgebraIVInfiniteGroups.LinearGroupsWith9FiguresContentsI.InfiniteGroupsA.Yu.Ol'shanskij,A.L.Shmerkin1II.LinearGroupsA.E.Zalesskij97AuthorIndex197SubjectIndex201I.InfiniteGroupsA.Yu.Ol'shanskij,A.L.Shmei'kinTranslatedfromt

2、heRussianbyJ.WiegoldContentsIntroduction3Chapter1.CombinatorialGroupTheory5§1.FreeGroups51.1.DefinitionofFreeGroup51.2.SubgroupsofFreeGroups61.3.Nielsen'sMethod.AutomorphismsofFreeGroups71.4.OtherRealisationsofFreeGroups9§2.DefiningRelationsandFreeConstruction

3、s112.1.PresentationsofGroups112.2.FreeConstructions14§3.PropertiesofFreeConstructions163.1.SubgroupsofFreeProductswithAmalgamationandHNN-Extensions163.2.FreeConstructionsasTransformationGroups173.3.BipolarStructures193.4.GroupsActingonTrees20§4.FinitelyPresent

4、edGroups224.1.ClassicalAlgorithmicProblemsinGroupTheory224.2.One-RelatorGroups244.3.SomeClassesofFinitelyPresentedGroups26§5.CancellationTheory295.1.GroupswithSmallCancellationConditions295.2.AGeometricalInterpretationoftheDeductionofConsequencesofDefiningRela

5、tions305.3.ResultsofNovikovandAdianonPeriodicGroups325.4.TopologicalApproachestotheConstructionofGroupswithGivenProperties332A.Yu.Ol'shanskij,A.L.Shmel'kin§6.OtherCombinatorialProblems356.1.EquationsoverGroups356.2.EquationsinaFreeGroup366.3.GrowthFunctionsofG

6、roups37Chapter2.StructureTheoryofInfiniteGroups40§1.AbelianGroups411.1.FinitelyGeneratedAbelianGroups421.2.Divisible(Complete)AbelianGroups431.3.PeriodicAbelianGroups451.4.TorsionfreeAbelianGroups461.5.ExtensionsintheClassofAbelianGroups481.6.AlgebraicallyComp

7、actGroups49§2.GroupExtensionsandHomologicalQuestions512.1.SemidirectProductsandWreathProducts512.2.Factor-SystemsandtheSecondCohomologyGroup532.3.DefinitionofHomologyandCohomologyGroups552.4.CohomologicalDimensionandOtherInvariants57§3.SolubleGroups593.1.Gener

8、alRemarks593.2.PolycyclicGroups603.3.SolubleGroupsofFiniteRank613.4.MetabelianGroupsandRelatedGroups633.5.GeneralisedSolubility653.6.IdentitiesinSolubleGroupsandAlgorithmicQuestion