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

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

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 *A*_{5} 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* A*_{5}, 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.

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