ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2017. Vol. 20

On Periodic Groups and Shunkov Groups that are Saturated by Dihedral Groups and A5

A. A. Shlepkin

A group is said to be periodic, if any of its elements is of finite order. A Shunkov group is a group in which any pair of conjugate elements generates Finite subgroup with preservation of this property when passing to factor groups by finite Subgroups. The group G is saturated with groups from the set of groups X if any A finite subgroup K of G is contained in the subgroup of G, Isomorphic to some group in X. The paper establishes the structure of periodic groups And Shunkov groups saturated by the set of groups M consisting of one finite simple non-Abelian group A5 and dihedral groups with Sylow 2-subgroup of order 2. It is proved that A periodic group saturated with groups from M, is either isomorphic to a prime Group A5, or is isomorphic to a locally dihedral group with Sylow 2 subgroup of order 2. Also, the existence of the periodic part of the Shunkov group saturated with groups from the set M is proved, and the structure of this periodic part is established.

Periodic groups, groups saturated with the set of groups, Shunkov group

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