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[5℄ TaylorM.A.,Ageneralization ofatheorem ofBelousov,Bull.Lond.Math.So

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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.

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