Existentially Closed Groups

174 Pages·1988·1.989 MB·English

by  Graham Higman, Elizabeth Scott

LONDONM ATHEMATICSAOLC IETMYO NOGRAPHS
NEW SERIES
SerEideist ors
P.M .C ohnB .E .J ohnson
LONODNM ATHEMATSIOCCAILE TMYO NGORAPHS
NEWS ERIES
Prevviooluuostfm hees MLoMnSo gwreaprpueishb hslbe yAd ac demic
Pretwsohs oamle ln qiuesishr obuaeld dd resseidn .N tehVweo lumes
Serwiibelpeslu is bhlbeydO x rfdoU nivertshirtyoo utuPthgwr ehoe rslsd .
NEWS ERIES
l.Di ophiannetiqituniRaee.l s B Cka.e r
2.T hSec hmuurl tiGprleigKoearrry p ilovsky
3.E xisltlceyln ogtsrieoaduG prsa hHaimg maanEndl izSacboettth
Existentially Closed
Groups
GrahaHmi gman
MatheImnast,ti ictault e
UnivoefOrx srfidoty
and
ElizaSbceottht
DeparotfMm aetnhte matics,
ThAesu rtalNiaatniU onniavle rsity
CLARENDON PRESS OXFORD
·
1988
OxfoUrndi vePrrsesisWty,a ltSotrne eOtx,f oOrXd26 DP
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PetaJlianygSa ingapHoorneKg o ngT okyo
NairoDbaire sS alaaCma pTeo wn
MelbouArnuec kland
anasds ociactoemdp ainni es
BeirBuetr lIibna daNni cosia
Oxfoisr dta r amdaer okfO xfoUrndi vePrrseistys
Publisihnte hdUe n itSetda tes
byO xfoUrndi vePrrseiNstyes w,Y ork
©GrahaHmi gmaannEd li zabSectoh1t 9t8,8
Alrli grhetss ervNeopd a,r otft hpisu blicmaatybi ero enp roduced,
stoirnea rd e triseyvsatloe rtrm a,ns mititnae ndfy,o rmo rb ya nmye ans,
electmreocnhiacn,pi hcoatlo,c orpeycionrgod,rio ntgh,e rwwiisteh,o ut
thper ipoerrm issoifoO nx foUrndi vePrrseistys
BritisLhi brCaaryt aloignPu uibnlgi cdaattiao n
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Existenctilaolgslreyod u -(pLso.n don
MathemaStoiccimaeoltyn ograNpehwss e.r ies;
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1.G roupTsh,e ooryf
I.T itIIl.eS coEttl,i zabIIeIt.Sh e ries
512'.2Q2A 171
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LibroafCry o ngrCeastsa liongP iunbgl icDaattiao n
HigmaGn.(. G raham)
Existenctilaolgslreyod u ps.
(LondMoant hemaStioccaimleo tyn ogranpehwss e;r .,
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Bibliogpr.a phy:
Incliunddeesx .
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Preface
Thbiso ogkr ewo faoc uotu orfls eec tguirvbeeyGsn r ahHaimg man
durtihnaegc adyeem1ai8r9c3 1 9-8t4h,e yleoaafsr t th einsou fr et he
WaynfPlreeostfseo orfsP huirMpea themaattt hiUecn sis vieotrfy
Oxf.oT rhdceo uwrasgsei vaesn i annt roductiocnl otsoe de xistentially
grouapnwsda, is n tetnobd eoe fid n tteora enmsyat t hteimcwaiiaatnnh
intiergnre ostuthp e oorlr oygw ihcia,ll bese oi negs saticobc lfier st-year
gradsutautd.Tee h nbeto sorke fltehcaiti.ssm
Thteh yeo ofer xisatlcellnyot gsireodiu ospfi s n tieinrte ssr tio gwhnt ;
anidht a asni nterheissottfcio hnragyn rgeilnagt wiiotnhsw hitidhpeesr
mathteimdcaiasllci ionpfweh si icftho ramp sa. rI tni tbse ginintnih neg ,
hanodBfs .H . N eumaannWdn. RS.c oitftrto m,ep dao rtfth teh yeo ofr
infignriot.Aue pn sgMuasc inatmyoorntegrh, sm e,a dieatp raotfm odel
thye;oa rnd M. iZnai f neudgalmeerwn,ot rtakrl,ao mnresdifit nto
recutrhsyeiB.oou rnst o me ofr etchweeon ritmvks oe rmreuy c ihtn h e
spiorftih etea ryleyao rfs s tuehbce.jTt encihquelso agfriruecos ames d
necaerbsysu,t p rtaihrmeay i mt ofii nsod u tths eo rotfts h itnhtgca sa n
goo ni tnh ien fignripotsuTe.h iitssr ufeoi,rn stoaftn hcieem ,p ortant
worokfK .H iciktnih nfii esla dna;dl ostfoh e owfRo. r PkEh .i lalnidp s,
otsh,ei rnt hcel orseellayat naedcd t fiievl(edn torte ahteerodef )
relaetxiivsetlceyln otgsirepaodsluI .lit ys alsspoio rftit hthen eso et es,
whoasieimn s o tp rteoass eynstt aecmocautnaitfi c n oifss hueebc;djbt ut
toa ssgirsottu hpie so(trrsae rscseht udoerne tsst abmlaitshhee­d
matictiofia ntndhs ew)ia iryn atc oo ronfte hres iuerbcw jth ihcahis t s
owcnh aracfltaevroaiunysrdet;w ti h ci crhe ciosg gnrizoatubhplye y.o r
Wed on ottrt yoi ncelvuedrey tthihaksitn n ogaw bno ut existentially
clogsreodwu epm se;rh eolptyeo tghireve eas dueffirc uinednetr standing
ofa,ni dn tienrt,ehs seute bt ctj oi nshpiitmror e e faudr thheirm sfeolrf .
Al iosoftr igsionuaarnlcfd eu sr rtehaeidrgsi i nvigetn nh b ei brlaip.oh gy
We ndooat s suanmpyer ikonro wloefld oggaein cdt harele lc ursive­
functthiyeto ohnrwa itbl enl e eidisen dc liutndh teeed. x t
A larogfte h biposa-oi rbksta soentd hw eo rokfM .Z ie,gt loegrether
with bywKo .Hr ikc akniAdn.M aci.nB tubytyrn eom eaanlslt hoefi r
mateircsio avleh re.erL dea rpgraeto sfZ ie'g(sl91 e8rp0a)p reerm ain
beyonsdc otophftee h bios.o F koerx amhpelg ei,va e dse tailed
classiofifc (at0th0,ie) o -ngi ecgn rpeo.sruH ic'k(si9 1n8)5p apdeird
vi Praecfe
noatp puenaatrfi ttlhe biro soh kab de werni nta,tn cedo nsenqouneen tly
oft hree souftl htpasat p aeriren clhued.rMe eadn oyt htehrih nagvse
beeonm itbtceeadua s ger oupe-ttivhcieaeolwr phoalisen udts to
conceonnatd riafftetery eopnfaet p pr.o ach
Somoeft hied eians b tohoaikr,sa e sf aarsw ea raew a,r enbeuwt;
mosotft hecmab nef ou,in nsdo mfeo romra nhoe,tir nea rwloir.ek rs
Gene,rw aedl oln yogti avcek nowliendt ghmee fntotserspx etc ific
theo,mr aenmoysfw hiacrhse t aitnde idff etreernmti, nc ooln,ot geyxt
angde nefrraotlmhio etr yil vg eiirnos.an s
Existcelnotgsireaodlwu lepyrs e difisrcsbutysS sceo(dt15 t91a )n d
B.H .N eum(an15n92& 1793.M) osotft hbea sriecsi untl htfiesr st
chahpetarererde u teot h.e m
Thsee ccohnadpi tbssea erd t hoen owfHo irckak niMdna cintyre
(918,0a )lthsooumogetfh h p er oaorfdesi ffnetr.e
Chap4ct oenrt maoisbntsasli ryce siurnle tcsu trhsei,woo hrniyc cahn
bef ouinandt extsbuoacosRhk o g(e91r6s.7 )
Three osftt h beo oibksa sberdo aodntl hwyeo rokfZ ie(g9l18e,0r )
althnoouatglt hlhr ee saurlheti, (ss f eoxrpa lm,Te heor5e.3am 1nsd
5.5a 1rdeu teoH icakniMdna cin(9t108y)r)Me.a noyft hteh reeoms
cabnef ouinZndi leegpra'psie anrl sm eoxsattc htsela ymf eo, rb mut in
somcea swees htaavkteeh nie d ebautstr etatheeddmir ffeen.It nl y
parutl,iZa ciredgolneeosrt dgiasmicegnuse s nsea rlalhl ig;osa f ma erse
playedt hfiuenn idcteoerd er ueolsAf.s a r eshuedl oten so t have
Rg-eingcer ro.uH poswreiv,ste h obuenl odt tehdoa ut(r 0 0,)- generic
existcelnotgsireaodlau lrpwyesh atl e,Za rineodgt h,ce arglseln eric
grposuS.o moef t hree s,uf lotrs exTahmeRp ellea tive-Subgroup
Theorem c(asloTlmheeGedte inmeersa lE mHbiegdTmdheaioennrm g,)
werep raolbvsyeoC d . MFil.le bru,Mt i lhlaensre vpeurb ltihsihse d
wo.r k
Thecsoem meanritens t eonndalesyad b rooaudt ,lt iogn ietvhee
reasdoemired o ewfah etrole o fooktr ho er igriens.Tau hllhet i ssyo tfo r
manoytf h erseesi uisln tvdsoF .lo verex palm,te hteh eotrhaeafi mtn itely
genegrraotiueespdm bedidenav beelrxeyi stcelnotgsireaoidluaf lpn y d
onilifyht a sso lvwaobrpldre o bwlateshm ce o mbrienseudwl otrb kyo f
Neum(a17n93n,S) imm(o17n93,sa) nMda ci(nt17by29)ra;ens do moef
thied eianCs h ap9to erri gwiinMtaahtc eidn( t17y92.raW e)ec aonn ly
apologize inu naddevrtathnadecki eiffi nctfguao lsrtka lnwooafty s
givcirinetged v,we hne iriteus n doudbut.ea bly
Sevpeeroahplal vbeee ehne ldpufrutilhn wegr iotfti hnbigoos k b,u t
we wopualrdt ilciutkloeta hralPnyek t er n,nNw ehuomtsaiem ely
inetcetrdijuorntishnl ege cteunrseutsrhp eardto woefrcseo rdrae,nc dt e
madmeo rceo mhpernes.H ieba llegsaovv ea luaadbvldieuc reti hneg
wriotfti hnbigos o Wkew. o ualldls iotk ote h aLnakKc oiv ,af cotsrh e
manhyep lfudli scutshshaietao nntdsh s ee caountdhh aowdrh itlhee
findarlao fftt hb iosow kab se ipnrge piaCnra endb. e rra
Praecfe vii
Thbiosow ka s bieOngx ufnuo nrddfe nurd ifnrgoa mnS ERrCe asrech
gr,aa nntidwt a cso pmlewtheitdlh seee cond aafu letlhoowarst h hiepl d
thAeu strNaaltiiUaonnni avlei rCnsa inrtbaWye.e rw oullidtk ote h ank
bootfth h eisnes tiftoturht seiuioprntp s.o r
G.H.
Illinois
E.S .
Canberra
Octob1e9r8 6
Thearrteew p oat ricduelbtathrIsam tu satc knohwel.reO ednigetse o
WilHfordie,dgsw hroe -awmayki ennteeidrnt e hssiutseb c,jwt hehne
lecttuotr heAedb erdmeeeento iftn hgBei r tMiasthh emCaotlilcoa­l
qui,iu nmA pr1i89l.3H aIdn ofto utnhdta atsl tki mgu,Ilw aotuilnd
certnaohitan vlleey c tountr hepidas r tic.uT lhsaeer c otno,dop f i dcebt
cou,ir tssom e yc o-hao,uDr trE . SAc..oA tsot irgidnealleildtvy,he er
lectwuerrveeers ro yu hgeh.w nleI fcth uoonufnkt es c aercsyos nnecting
matetrhileae lvo;ef pl r evkinoouwsl wehdigIcae hs suomfme yd
audience avnaudrn issetyde mwaiatdniIedcm l aaylda len y u;m boefr
underlaimtbiekes et.Tsa htea osfkr edutchiminesgs t sos omething
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fetehlwa htas thh eap sr odduecseewdre voletflsh m ea themat,i cal public
Iw ounlodct o nttihfinecu teoi fpo unt mtyin nagm, e whie,tro hsnt he
tiptalogefwe h airtse ahlewlroy .r )k
G.H.