On periodic groups with a narrow conjugacy class of involutions

Yu. Mao^a, X. Ma^a, D. V. Lytkina^b, V. D. Mazurov<sup>c

a</sup> School of Mathematics and Statistics, ShanXi DaTong University, Datong, Shanxi, 037009, P.R. China
^b Novosibirsk State University, Novosibirsk, Russia
^c Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: In a 2000 paper, Mazurov studied periodic groups containing involutions (elements of order $2$) whose centralizers are abelian $2$-groups. That work provided a description of such groups under the assumption that they include a noncyclic subgroup of order $4$. In the present paper, we consider the case where the centralizers of involutions of the group are locally cyclic $2$-groups.

Keywords: periodic group, involution, centralizer, locally finite group.

UDC: 512.542

MSC: 35R30

Received: 09.06.2025
Revised: 09.06.2025
Accepted: 12.06.2025

DOI: 10.33048/smzh.2025.66.512

 English version: Siberian Mathematical Journal, 2025, 66:5, 1231–1234