2011/02/17 by Victor Shcherbacov, V. A. Shcherbacov, Shcherbacov, V. A.
Engineering · Mathematics · #20N05 #Advanced Mathematical Theories #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #graph theory and CDMA systems #math.GR #msc:20N05
paper · pdf · doi:10.48550/arxiv.1102.3525
55 pages
arxiv created 2011/02/17 · openalex publication_date 2011/02/17 · arxiv updated 2011/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.