Groups: Topological, Combinatorial and Arithmetic Aspects PDF
Preview Groups: Topological, Combinatorial and Arithmetic Aspects
LONDONMATHEMATICALSOCIETYLECTURENOTESERIES ManagingEditor:ProfessorN.J.Hitchin,MathematicalInstitute, UniversityofOxford,24–29StGiles,OxfordOX13LB,UnitedKingdom Thetitlesbelowareavailablefrombooksellers,or,incaseofdifficulty,fromCambridgeUniversityPressatwww.cambridge.org. 148 Helicesandvectorbundles, A.N.RUDAKOVetal 149 Solitons,nonlinearevolutionequationsandinversescattering, M.ABLOWITZ&P.CLARKSON 150 Geometryoflow-dimensionalmanifolds1, S.DONALDSON&C.B.THOMAS(eds) 151 Geometryoflow-dimensionalmanifolds2, S.DONALDSON&C.B.THOMAS(eds) 152 Oligomorphicpermutationgroups, P.CAMERON 153 L-functionsandarithmetic, J.COATES&M.J.TAYLOR(eds) 155 Classificationtheoriesofpolarizedvarieties, TAKAOFUJITA 158 GeometryofBanachspaces, P.F.X.MU¨LLER&W.SCHACHERMAYER(eds) 159 GroupsStAndrews1989volume1, C.M.CAMPBELL&E.F.ROBERTSON(eds) 160 GroupsStAndrews1989volume2, C.M.CAMPBELL&E.F.ROBERTSON(eds) 161 Lecturesonblocktheory, BURKHARDKU¨LSHAMMER 163 Topicsinvarietiesofgrouprepresentations, S.M.VOVSI 164 Quasi-symmetricdesigns, M.S.SHRIKANDE&S.S.SANE 166 Surveysincombinatorics,1991, A.D.KEEDWELL(ed) 168 Representationsofalgebras, H.TACHIKAWA&S.BRENNER(eds) 169 Booleanfunctioncomplexity, M.S.PATERSON(ed) 170 ManifoldswithsingularitiesandtheAdams-Novikovspectralsequence, B.BOTVINNIK 171 Squares, A.R.RAJWADE 172 Algebraicvarieties, GEORGER.KEMPF 173 Discretegroupsandgeometry, W.J.HARVEY&C.MACLACHLAN(eds) 174 Lecturesonmechanics, J.E.MARSDEN 175 Adamsmemorialsymposiumonalgebraictopology1, N.RAY&G.WALKER(eds) 176 Adamsmemorialsymposiumonalgebraictopology2, N.RAY&G.WALKER(eds) 177 Applicationsofcategoriesincomputerscience, M.FOURMAN,P.JOHNSTONE&A.PITTS(eds) 178 LowerK-andL-theory, A.RANICKI 179 Complexprojectivegeometry, G.ELLINGSRUDetal 180 LecturesonergodictheoryandPesintheoryoncompactmanifolds, M.POLLICOTT 181 GeometricgrouptheoryI, G.A.NIBLO&M.A.ROLLER(eds) 182 GeometricgrouptheoryII, G.A.NIBLO&M.A.ROLLER(eds) 183 Shintanizetafunctions, A.YUKIE 184 Arithmeticalfunctions, W.SCHWARZ&J.SPILKER 185 Representationsofsolvablegroups, O.MANZ&T.R.WOLF 186 Complexity:knots,colouringsandcounting, D.J.A.WELSH 187 Surveysincombinatorics,1993, K.WALKER(ed) 188 Localanalysisfortheoddordertheorem, H.BENDER&G.GLAUBERMAN 189 Locallypresentableandaccessiblecategories, J.ADAMEK&J.ROSICKY 190 Polynomialinvariantsoffinitegroups, D.J.BENSON 191 Finitegeometryandcombinatorics, F.DECLERCKetal 192 Symplecticgeometry, D.SALAMON(ed) 194 Independentrandomvariablesandrearrangementinvariantspaces, M.BRAVERMAN 195 Arithmeticofblowupalgebras, WOLMERVASCONCELOS 196 Microlocalanalysisfordifferentialoperators, A.GRIGIS&J.SJO¨STRAND 197 Two-dimensionalhomotopyandcombinatorialgrouptheory, C.HOG-ANGELONIetal 198 Thealgebraiccharacterizationofgeometric4-manifolds, J.A.HILLMAN 199 InvariantpotentialtheoryintheunitballofCn, MANFREDSTOLL 200 TheGrothendiecktheoryofdessinsd’enfant, L.SCHNEPS(ed) 201 Singularities, JEAN-PAULBRASSELET(ed) 202 Thetechniqueofpseudodifferentialoperators, H.O.CORDES 203 HochschildcohomologyofvonNeumannalgebras, A.SINCLAIR&R.SMITH 204 Combinatorialandgeometricgrouptheory, A.J.DUNCAN,N.D.GILBERT&J.HOWIE(eds) 205 Ergodictheoryanditsconnectionswithharmonicanalysis, K.PETERSEN&I.SALAMA(eds) 207 GroupsofLietypeandtheirgeometries, W.M.KANTOR&L.DIMARTINO(eds) 208 Vectorbundlesinalgebraicgeometry, N.J.HITCHIN,P.NEWSTEAD&W.M.OXBURY(eds) 209 Arithmeticofdiagonalhypersurfacesoverinfitefields, F.Q.GOUVEA&N.YUI 210 HilbertC∗-modules, E.C.LANCE 211 Groups93Galway/StAndrewsI, C.M.CAMPBELLetal(eds) 212 Groups93Galway/StAndrewsII, C.M.CAMPBELLetal(eds) 214 GeneralisedEuler-Jacobiinversionformulaandasymptoticsbeyondallorders, V.KOWALENKOetal 215 Numbertheory1992–93, S.DAVID(ed) 216 Stochasticpartialdifferentialequations, A.ETHERIDGE(ed) 217 Quadraticformswithapplicationstoalgebraicgeometryandtopology, A.PFISTER 218 Surveysincombinatorics,1995, PETERROWLINSON(ed) 220 Algebraicsettheory, A.JOYAL&I.MOERDIJK 221 Harmonicapproximation, S.J.GARDINER 222 Advancesinlinearlogic, J.-Y.GIRARD,Y.LAFONT&L.REGNIER(eds) 223 Analyticsemigroupsandsemilinearinitialboundaryvalueproblems, KAZUAKITAIRA 224 Computability,enumerability,unsolvability, S.B.COOPER,T.A.SLAMAN&S.S.WAINER(eds) 225 Amathematicalintroductiontostringtheory, S.ALBEVERIO,J.JOST,S.PAYCHA,S.SCARLATTI 226 Novikovconjectures,indextheoremsandrigidityI, S.FERRY,A.RANICKI&J.ROSENBERG(eds) 227 Novikovconjectures,indextheoremsandrigidityII, S.FERRY,A.RANICKI&J.ROSENBERG(eds) 228 ErgodictheoryofZdactions, M.POLLICOTT&K.SCHMIDT(eds) 229 Ergodicityforinfinitedimensionalsystems, G.DAPRATO&J.ZABCZYK 230 Prolegomenatoamiddlebrowarithmeticofcurvesofgenus2, J.W.S.CASSELS&E.V.FLYNN 231 Semigrouptheoryanditsapplications, K.H.HOFMANN&M.W.MISLOVE(eds) 232 ThedescriptivesettheoryofPolishgroupactions, H.BECKER&A.S.KECHRIS 233 Finitefieldsandapplications, S.COHEN&H.NIEDERREITER(eds) 234 Introductiontosubfactors, V.JONES&V.S.SUNDER 235 Numbertheory1993–94, S.DAVID(ed) 236 TheJamesforest, H.FETTER&B.GAMBOADEBUEN 237 Sievemethods,exponentialsums,andtheirapplicationsinnumbertheory, G.R.H.GREAVESetal 238 Representationtheoryandalgebraicgeometry, A.MARTSINKOVSKY&G.TODOROV(eds) 239 Cliffordalgebrasandspinors, P.LOUNESTO 240 Stablegroups, FRANKO.WAGNER 241 Surveysincombinatorics,1997, R.A.BAILEY(ed) 242 GeometricGaloisactionsI, L.SCHNEPS&P.LOCHAK(eds) 243 GeometricGaloisactionsII, L.SCHNEPS&P.LOCHAK(eds) 244 Modeltheoryofgroupsandautomorphismgroups, D.EVANS(ed) 245 Geometry,combinatorialdesignsandrelatedstructures, J.W.P.HIRSCHFELDetal 246 p-Automorphismsoffinitep-groups, E.I.KHUKHRO 247 Analyticnumbertheory, Y.MOTOHASHI(ed) 248 Tametopologyando-minimalstructures, LOUVANDENDRIES 249 Theatlasoffinitegroups:tenyearson, ROBERTCURTIS&ROBERTWILSON(eds) 250 Charactersandblocksoffinitegroups, G.NAVARRO 251 Gro¨bnerbasesandapplications, B.BUCHBERGER&F.WINKLER(eds) 252 Geometryandcohomologyingrouptheory, P.KROPHOLLER,G.NIBLO,R.STO¨HR(eds) 253 Theq-Schuralgebra, S.DONKIN 254 Galoisrepresentationsinarithmeticalgebraicgeometry, A.J.SCHOLL&R.L.TAYLOR(eds) 255 Symmetriesandintegrabilityofdifferenceequations, P.A.CLARKSON&F.W.NIJHOFF(eds) 256 AspectsofGaloistheory, HELMUTVO¨LKLEINetal 257 Anintroductiontononcommutativedifferentialgeometryanditsphysicalapplications2ed, J.MADORE 258 Setsandproofs, S.B.COOPER&J.TRUSS(eds) 259 Modelsandcomputability, S.B.COOPER&J.TRUSS(eds) 260 GroupsStAndrews1997inBath,I, C.M.CAMPBELLetal 261 GroupsStAndrews1997inBath,II, C.M.CAMPBELLetal 263 Singularitytheory, BILLBRUCE&DAVIDMOND(eds) 264 Newtrendsinalgebraicgeometry, K.HULEK,F.CATANESE,C.PETERS&M.REID(eds) 265 Ellipticcurvesincryptography, I.BLAKE,G.SEROUSSI&N.SMART 267 Surveysincombinatorics,1999, J.D.LAMB&D.A.PREECE(eds) 268 Spectralasymptoticsinthesemi-classicallimit, M.DIMASSI&J.SJO¨STRAND 269 Ergodictheoryandtopologicaldynamics, M.B.BEKKA&M.MAYER 270 AnalysisonLieGroups, N.T.VAROPOULOS&S.MUSTAPHA 271 Singularperturbationsofdifferentialoperators, S.ALBEVERIO&P.KURASOV 272 Charactertheoryfortheoddorderfunction, T.PETERFALVI 273 Spectraltheoryandgeometry, E.B.DAVIES&Y.SAFAROV(eds) 274 TheMandelbrotset,themeandvariations, TANLEI(ed) 275 Computationalandgeometricaspectsofmodernalgebra, M.D.ATKINSONetal(eds) 276 Singularitiesofplanecurves, E.CASAS-ALVERO 277 Descriptivesettheoryanddynamicalsystems, M.FOREMANetal(eds) 278 Globalattractorsinabstractparabolicproblems, J.W.CHOLEWA&T.DLOTKO 279 Topicsinsymbolicdynamicsandapplications, F.BLANCHARD,A.MAASS&A.NOGUEIRA(eds) 280 CharactersandAutomorphismGroupsofCompactRiemannSurfaces, T.BREUER 281 Explicitbirationalgeometryof3-folds, ALESSIOCORTI&MILESREID(eds) 282 Auslander-Buchweitzapproximationsofequivariantmodules, M.HASHIMOTO 283 Nonlinearelasticity, R.OGDEN&Y.FU(eds) 284 Foundationsofcomputationalmathematics, R.DEVORE,A.ISERLES&E.SULI(eds) 285 Rationalpointsoncurvesoverfinitefields:TheoryandApplications, H.NIEDERREITER&C.XING 286 Cliffordalgebrasandspinors2ndedn, P.LOUNESTO 287 TopicsonRiemannsurfacesandFuchsiangroups, E.BUJALANCE,A.F.COSTA&E.MARTINEZ(eds) 288 Surveysincombinatorics,2001, J.W.P.HIRSCHFELD(ed) 289 AspectsofSobolev-typeinequalities, L.SALOFF-COSTE 290 QuantumgroupsandLietheory, A.PRESSLEY 291 Titsbuildingsandthemodeltheoryofgroups, K.TENT 292 Aquantumgroupsprimer, S.MAJID 293 SecondorderpartialdifferentialequationsinHilbertspaces, G.DAPRATO&J.ZABCZYK 294 Introductiontooperatorspacetheory, G.PISIER 295 Geometryandintegrability, L.MASON&Y.NUTKU(eds) 296 Lecturesoninvarianttheory, I.DOLGACHEV 297 Thehomotopycategoryofsimplyconnected4-manifolds, H.-J.BAUES 298 Higheroperads,highercategories, T.LEINSTER 299 Kleiniangroupsandhyperbolic3-manifolds, Y.KOMORI,V.MARKOVIC&C.SERIES(eds) 300 IntroductiontoMo¨biusdifferentialgeometry, U.HERTRICH-JEROMIN 301 StablemodulesandtheD(2)-problem, F.E.A.JOHNSON 302 DiscreteandcontinuousnonlinearSchro¨dingersystems, M.ABLOWITZ,B.PRINARI&D.TRUBATCH 304 GroupsStAndrews2001inOxfordv1, C.M.CAMPBELL,E.F.ROBERTSON&G.C.SMITH(eds) 305 GroupsStAndrews2001inOxfordv2, C.M.CAMPBELL,E.F.ROBERTSON&G.C.SMITH(eds) 306 Peyresqlecturesongeometricmechanicsandsymmetry, J.MONTALDI&T.RATIU(eds) 307 Surveysincombinatorics2003, C.D.WENSLEY(ed) LondonMathematicalSocietyLectureNoteSeries.311 Groups Topological, Combinatorial and Arithmetic Aspects Editedby T.W.Mu¨ller QueenMary,UniversityofLondon publishedbythepresssyndicateoftheuniversityofcambridge ThePittBuilding,TrumpingtonStreet,Cambridge,UnitedKingdom cambridgeuniversitypress TheEdinburghBuilding,CambridgeCB22RU,UK 40West20thStreet,NewYork,NY10011-4211,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia RuizdeAlarco´n13,28014Madrid,Spain DockHouse,TheWaterfront,CapeTown8001,SouthAfrica http://www.cambridge.org (cid:2)C CambridgeUniversityPress2004 Thisbookisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithout thewrittenpermissionofCambridgeUniversityPress. Firstpublished2004 PrintedintheUnitedKingdomattheUniversityPress,Cambridge TypefaceTimes.10/13pt. SystemLATEX2ε [tb] ArecordforthisbookisavailablefromtheBritishLibrary ISBN0521542871paperback Contents Listofauthorsandparticipants page vii Preface xi 1 Reductivegroupsasmetricspaces 1 H.Abels 2 Finitenesspropertiesofgroupsactingontwinbuildings 21 P.Abramenko 3 HigherfinitenesspropertiesofS-arithmeticgroups inthefunctionfieldcaseI 27 H.Behr 4 Controlledtopologyandgroupactions 43 R.BieriandR.Geoghegan 5 FinitenesspropertiesofsolubleS-arithmetic groups–Asurvey 64 K.-U.Bux 6 Topologyinpermutationgroups 93 P.J.Cameron 7 Eulercharacteristicsofdiscretegroups 106 I.M.Chiswell 8 IntersectionsofMagnussubgroupsofone-relatorgroups 255 D.J.Collins 9 Aminimalitypropertyofcertainbranchgroups 297 R.I.GrigorchukandJ.S.Wilson v vi Contents 10 Latticeswithnon-integralcharacter 306 H.Helling 11 Someapplicationsofprobabilityingrouptheory 318 A.Mann 12 ParitypatternsinHeckegroupsandFermatprimes 327 T.W.Mu¨ller 13 Automorphismsofthebinarytree:state-closedsubgroups anddynamicsof1/2-endomorphisms 375 V.NekrashevychandS.Sidki 14 Themappingclassgroupofthetwicepuncturedtorus 405 J.R.ParkerandC.Series 15 Kac–Moodygroups:splitandrelativetheories.Lattices 487 B.Remy 16 Onthefiniteimagesofinfinitegroups 542 D.Segal 17 Pseudo-finitegeneralizedtrianglegroups 564 E.B.VinbergandR.Kaplinsky Authors and participants H.Abels,Fakulta¨tfu¨rMathematik,Universita¨tBielefeld,POB100131, D-33501Bielefeld,Germany([email protected]) P.Abramenko,DepartmentofMathematics,UniversityofVirginia,POB 400137(KerchofHall),Charlottesville,VA22904,USA([email protected]) S.I.Adian,SteklovMathematicalInstitute,42ul.Vavilova,117966Moscow GSP-1,Russia([email protected]) H.Behr,FachbereichMathematik,J.W.Goethe-Universita¨t,POB111932, 60054Frankfurta.M.,Germany([email protected]) R.Bieri,FachbereichMathematik,J.W.Goethe-Universita¨t,POB111932, 60054Frankfurta.M.,Germany([email protected]) M.Bridson,DepartmentofMathematics,ImperialCollege,180Queen’s Gate,LondonSW72BZ,UK([email protected]) K.-U.Bux,DepartmentofMathematics,CornellUniversity,MalottHall310, Ithaka,NY19853-4201,USA(bux [email protected]) P.J.Cameron,SchoolofMathematicalSciences,QueenMary,Universityof London,MileEndRoad,LondonE14NS,UK([email protected]) I.M.Chiswell,SchoolofMathematicalSciences,QueenMary,Universityof London,MileEndRoad,LondonE14NS,UK([email protected]) D.J.Collins,SchoolofMathematicalSciences,QueenMary,Universityof London,MileEndRoad,LondonE14NS,UK([email protected]) A.Dress,Fakulta¨tfu¨rMathematik,Universita¨tBielefeld,POB100131, D-33501Bielefeld,Germany([email protected]) vii viii Listofauthorsandparticipants R.Geoghegan,DepartmentofMathematicalSciences,SUNY,Binghamton, NY13902-6000,USA([email protected]) R.I.Grigorchuk,SteklovMathematicalInstitute,GubkinaStreet8,Moscow 117966,Russia([email protected])andDepartmentofMathematics,Texas A&MUniversity,CollegeStation,Texas77843-3368,USA ([email protected]) F.Grunewald,MathematischesInstitut,Heinrich-HeineUniversita¨t,D-40225 Du¨sseldorf,Germany([email protected]) H.Helling,Fakulta¨tfu¨rMathematik,Universita¨tBielefeld,POB100131, D-33501Bielefeld,Germany([email protected]) W.Imrich,InstituteofAppliedMathematics,Montanuniversita¨tLeoben, A-8700Leoben,Austria([email protected]) R.Kaplinsky,JerusalemORTCollege,GivatRam,PB39161,Jerusalem 91390,Israel([email protected]) I.Lysionok,SteklovMathematicalInstitute,42ul.Vavilova,117966Moscow GSP-1,Russia([email protected]) A.Mann,InstituteofMathematics,TheHebrewUniversity,GivatRam, Jerusalem91904,Israel([email protected]) J.Mennicke,Fakulta¨tfu¨rMathematik,Universita¨tBielefeld,POB100131, D-33501Bielefeld,Germany([email protected]) T.W.Mu¨ller,SchoolofMathematicalSciences,QueenMary,Universityof London,MileEndRoad,LondonE14NS,UK([email protected]) V.Nekrashevych,FacultyofMechanicsandMathematics,KyivTaras ShevchenkoUniversity,vul.Volodymyrska,60,Kyiv,01033,Ukraine ([email protected]) J.R.Parker,DepartmentofMathematicalSciences,UniversityofDurham, DurhamDH13LE,UK([email protected]) L.Reeves,MathematicalInstitute,UniversityofOxford,24–29StGiles’, OxfordOX13LB,UK([email protected]) U.Rehmann,Fakulta¨tfu¨rMathematik,Universita¨tBielefeld,POB100131, D-33501Bielefeld,Germany([email protected]) B.Remy,InstitutFourier–UMR5582,UniversiteGrenoble1–Joseph Fourier,100ruedesmaths,BP74–38402Saint-Martind’Heres,France ([email protected]) Listofauthorsandparticipants ix D.Segal,AllSoulsCollege,OxfordOX14AL,UK ([email protected]) C.M.Series,MathematicsInstitute,UniversityofWarwick,Coventry CV47AL,UK([email protected]) S.N.Sidki,DepartamentodeMatema´tica,UniversidadedeBras´ılia, Bras´ılia-Df,70.910-900,Brazil([email protected]) E.B.Vinberg,DepartmentofMechanicsandMathematics,MoscowState University,Leninskiegory,119899Moscow,Russia ([email protected]) J.S.Wilson,SchoolofMathematicsandStatistics,UniversityofBirmingham, Edgbaston,BirminghamB152TT,UK([email protected])
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