Groups: Topological, Combinatorial and Arithmetic Aspects

603 Pages·2004·2.78 MB·English

by  T. W. Muller

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])