V. A. Shcherbacov. A-nuclei and A-centers of a quasigroup
Submitted on: Apr 08, 2012, 22:29:01
Natural Sciences / Mathematics / Graph theory
Description: A-nuclei (groups of regular permutations) of a quasigroup are studied. A quasigroup is A-nuclear if and only if it is group isotope. Any quasigroup with permutation medial or paramedial identity is an abelian group isotope. Definition of A-center of a quasigroup is given. A quasigroup is A-central if and only if it is abelian group isotope. If a quasigroup is central in Belyavskaya-Smith sense, then it is A-central. Conditions when A-nucleus define normal congruence of a quasigroup are established, conditions normality of nuclei of some inverse quasigroups are given. Notice, definition of A-nucleus of a loop and A-center of a loop coincides, in fact, with corresponding standard definition.
The abstract of this article has been published in the "Intellectual Archive Bulletin" , April 2012, ISSN 1929-1329.
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