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Article

Phillips, J. D. ; Smith, J. D. H.
The endocenter and its applications to quasigroup representation theory. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 32 (1991), issue 3, pp. 417-422
MSC: 20E07, 20E10, 20F14, 20N05 | MR 1159788 | Zbl 0748.20016
Keywords:
multiplication group; quasigroup; center
Summary:
A construction is given, in a variety of groups, of a ``functorial center'' called the endocenter. The endocenter facilitates the identification of universal multiplication groups of groups in the variety, addressing the problem of determining when combinatorial multiplication groups are universal.
References:
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[MKS] Magnus W., Karrass A., Solitar D.: Combinatorial Group Theory. New York, Dover, 1976. MR 0422434 | Zbl 1130.20307
[Ne] Neumann H.: Varieties of Groups. Berlin, Springer-Verlag, 1967. MR 0215899 | Zbl 0251.20001
[Rb] Robinson D.J.S.: A Course in The Theory of Groups. New York, Springer-Verlag, 1982. MR 0648604 | Zbl 0836.20001
[Sm] Smith J.D.H.: Representation Theory of Infinite Groups and Finite Quasigroups. Montréal, Les Presses de l'Université de Montréal, 1986. MR 0859373 | Zbl 0609.20042
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