Groups with restrictions on normal subgroups

A. I. Budkin

Altai State University, Barnaul

Abstract: It is proved that if $G$ is a group without elements of order $2$, and the normal closure of every $2$-generated subgroup of $G$ is a nilpotent group of class at most $3$, then $G$ will be a nilpotent group of class at most $4$. It is also shown that the restriction on second-order elements cannot be lifted.

Keywords: nilpotent group, normal closure of subgroup, Levi class, variety, quasivariety.

UDC: 512.544

Received: 19.01.2023
Revised: 04.12.2024

DOI: 10.33048/alglog.2024.63.101

 English version: Algebra and Logic, 2024, 63:1, 1–9