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Algebra Logika, 2024 Volume 63, Number 3, Pages 323–337 (Mi al2810)

Locally finite groups containing direct products of dihedral groups

A. A. Shlepkin

Siberian Federal University, Krasnoyarsk

Abstract: Let $d$ be a fixed natural number. We prove the following: THEOREM. Let $G$ be a locally finite group saturated with groups from a set $\mathfrak{M}$ consisting of direct products of $d$ dihedral groups. Then $G$ is a direct product of $d$ groups of the form $B\leftthreetimes\langle v\rangle$, where $B$ is a locally cyclic group inverted by an involution $v$.

Keywords: locally finite group, direct products of dihedral groups, locally cyclic group, involution.

UDC: 512.544.5

Received: 07.07.2024
Revised: 11.04.2025

DOI: 10.33048/alglog.2024.63.307


 English version:
Algebra and Logic, 2024, 63:3, 217–227


© Steklov Math. Inst. of RAS, 2026