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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2022 Volume 28, Number 1, Pages 239–246 (Mi timm1895)

On periodic completely splittable groups

A. I. Sozutov

Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk

Abstract: We study an infinite periodic group $G$ with involutions that coincides with the set-theoretic union of a collection of proper locally cyclic subgroups with trivial pairwise intersections. It is proved that if $G$ contains an elementary subgroup $E_8$, then either $G$ is locally finite (and its structure is described) or its subgroup $O_2(G)$ is elementary and strongly isolated in $G$. If $G$ has a finite element of order greater than 2 and the $2$-rank of $G$ is not $2$, then $G$ is locally finite, and its structure is described.

Keywords: periodic group, completely splittable group, $2$-rank of a group, strongly isolated subgroup, finite element.

UDC: 512.54

MSC: 20E28, 20F50

Received: 10.10.2021
Revised: 16.12.2021
Accepted: 20.12.2021

DOI: 10.21538/0134-4889-2022-28-1-239-246



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