On periodic completely splittable groups

A. I. Sozutov

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 1, pp. 239-246

Résumé

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.

Détail

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

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