This article is cited in 4 papers

A Levi class generated by a quasivariety of nilpotent groups

V. V. Lodeishchikova

Altai State University, Barnaul

Abstract: Let $L(M)$ be a class of all groups $G$ in which the normal closure of any element belongs to $M$; $qM$ is a quasivariety generated by a class $M$.
We consider a quasivariety $qH_2$ generated by a relatively free group in a class of nilpotent groups of class at most $2$ with commutator subgroup of exponent $2$. It is proved that the Levi class $L(qH_2)$ generated by the quasivariety $qH_2$ is contained in the variety of nilpotent groups of class at most $3$.

Keywords: group, nilpotent group, variety, quasivariety, Levi class.

UDC: 512.54.01

Received: 03.07.2018
Revised: 08.11.2019

DOI: 10.33048/alglog.2019.58.405

 English version: Algebra and Logic, 2019, 58:4, 327–336

Bibliographic databases:

• 
•