拟群的A-核与A-中心
A-nuclei and A-centers of a quasigroup
摘要：
研究了拟群的A-核（正则置换群）。一个拟群是A-核的当且仅当它是群同位素。任何具有置换中间或参数恒等式的拟群都是阿贝尔群的同位素。给出了拟群的A-中心的定义。一个拟群是A-中心的当且仅当它是阿贝尔群同位素。如果一个拟群在Belyavskaya-Smith意义下是中心的，那么它是A-中心的。建立了A-核定义拟群正规同余的条件，给出了某些逆拟群的核正规的条件。请注意，环的A-核和环的A-中心的定义实际上与相应的标准定义一致。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
