Geodesic
On periodic groups and Shunkov groups that are saturated by dihedral groups and $A_5 $
The Bulletin of Irkutsk State University. Series Mathematics, Tome 20 (2017), pp. 96-108 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\mathfrak {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 $\mathfrak {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 $ \mathfrak {M} $ is proved, and the structure of this periodic part is established.
Keywords: periodic groups, groups saturated with the set of groups, Shunkov group. 
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     title = {On periodic groups and {Shunkov} groups that are saturated by dihedral groups and $A_5 $},
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A. A. Shlepkin. On periodic groups and Shunkov groups that are saturated by dihedral groups and $A_5 $. The Bulletin of Irkutsk State University. Series Mathematics, Tome 20 (2017), pp. 96-108. http://geodesic.mathdoc.fr/item/IIGUM_2017_20_a6/

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