Year: 2025
Type: article
Abstract: The Levi class L(M) generated by the class of groups M is the class of all groups in which the normal closure of each cyclic subgroup belongs to M. Let p be a prime number, p ̸= 2, s be a natural number, s ≥ 2, and s > 2 for p = 3; Hps be a free group of rank 2 in the variety of nilpotent groups of class ≤ 2 of exponent ps with commutator subgroup of exponent p; Z is an infinite cyclic group; q{Hps , Z} is a quasivariety generated by the set of groups {Hps , Z}. We find a basis of quasi-identities of the Levi class L(q{Hps , Z}) and establish that there exists a continuous set of quasivarieties K such that L(K) = L(q{Hps , Z}).
Author: S. A. Shakhova
Institution: Altai State University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410017944