A.A. Shlepkin. On a periodic part of a Shunkov group saturated with wreathed groups

A group $G$ is saturated with groups from a set of groups $\mathfrak{X}$ if any finite subgroup $K$ of $G$ is contained in a subgroup of $G$ isomorphic to some group from~$\mathfrak{X}$. A group $G$ is called a Shunkov group (a conjugately biprimitively finite group) if, for any finite subgroup $H$ of $G$, any two conjugate elements of prime order in the quotient group $N_G(H)/h$ generate a finite group. Let $G$ be a group. If all elements of finite orders from $G$ are contained in a periodic subgroup of $G$, then it is called a periodic part of $G$ and is denoted by $t(G)$. It is known that a Shunkov group may have no periodic part. The existence of a periodic part of a Shunkov group saturated with finite wreathed groups is proved and the structure of the periodic part is established.

Keywords: group saturated with a set of groups, Shunkov group

The paper was received by the Editorial Office on Juny 5, 2018.

Funding Agency: This work was supported by the Russian Foundation for Basic Research (project no. 18-31-00257).

Aleksei Anatolievich Shlepkin, Cand. Sci (Phys.-Math.), Institute of Space and Information Technologies of Siberian Federal University, Krasnoyarsk, 660074 Russia, e-mail: shlyopkin@gmail.com


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