Realizations of Loops and Groups dened by short identities
Comment.Math.Univ.Carolin. 50,3 (2009)373{383.
Abstrat:Inareentpaper,thosequasigroupidentitiesinvolvingatmostthreevariables
andof\length"sixwhihforethequasigrouptobealooporgrouphavebeenenumerated
byomputer. Weseparatetheseidentitiesintosubsetsaordingtowhatlassesofloops
theydene and also providehumanly-omprehensibleproofs for most of the omputer-
generatedresults.
Keywords:quasigroupidentity,loop,group
AMSSubjetClassiation:20N05
Referenes
[1℄ BelousovV.D.,Balaned identities in quasigroups (inRussian), Mat. Sb.(N.S.) 70(112)
(1966),55{97.
[2℄ BelousovV.D.,Atheoremonbalanedidentities(inRussian),Mat.Issled.71(1983),22{24.
[3℄ Fiala N.C., Short identities implying that a quasigroup is a loop or group, Quasigroups
RelatedSystems15(2007),263{271.
[4℄ SadeA.,Entropiedemosiennede multigroupodesetdequasigroupes,Ann.So.Si.Brux-
elles,Ser.I,73(1959),302{309.
[5℄ TaylorM.A.,Ageneralization ofatheorem ofBelousov,Bull.Lond.Math.So.10(1978),
285{286.