On a periodic part of a Shunkov group saturated with wreathed groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 281-285
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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.
@article{TIMM_2018_24_3_a24,
author = {A. A. Shlepkin},
title = {On a periodic part of a {Shunkov} group saturated with wreathed groups},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {281--285},
publisher = {mathdoc},
volume = {24},
number = {3},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a24/}
}
A. A. Shlepkin. On a periodic part of a Shunkov group saturated with wreathed groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 281-285. http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a24/