On the Quasivarieties Generated by a Finite Group and Lacking Any Independent Bases of Quasi-Identities

Сибирский математический журнал

article

A. I. Budkin¹ 

[1] Altai State University

关键词: quasivariety;    quasi-identity;    independent basis;    nilpotent group;   

DOI  :  10.1134/S0037446620060038

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Let $ {\mathcal{R}}_{p^{k}} $ be the variety of $ 2 $ -nilpotent groups of exponent $ p^{k} $ with commutator subgroup of exponent $ p $ ( $ p $ is a prime). We prove the infinity of the set of the subquasivarieties of  $ {\mathcal{R}}_{p^{k}} $ $ (k\geq 2) $ generated by a finite group and lacking any independent bases of quasi-identities.

【 授权许可】

CC BY