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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2023 Volume 64, Number 4, Pages 733–741 (Mi smj7793)

Groups with nilpotent $n$-generated normal subgroups

A. I. Budkin

Altai State University, Barnaul

Abstract: Let $L_n({\mathcal N})$ be the class of all groups $G$ in which the normal closure of each $n$-generated subgroup of $G$ belongs to ${\mathcal N}$. It is known that if ${\mathcal N}$ is a quasivariety of groups then so is $L_n({\mathcal N})$. We find the conditions on ${\mathcal N}$ for the sequence $L_1({\mathcal N}),L_2({\mathcal N}),\dots $ to contain infinitely many different quasivarieties. In particular, such are the quasivarieties ${\mathcal N}$ generated by a finitely generated nilpotent nonabelian group.

Keywords: nilpotent group, quasivariety, axiomatic rank, Levi class.

UDC: 512.544

MSC: 35R30

Received: 23.03.2023
Revised: 16.04.2023
Accepted: 16.05.2023

DOI: 10.33048/smzh.2023.64.406



© Steklov Math. Inst. of RAS, 2025