On a periodic part of a Shunkov group saturated with wreathed groups

A group G is saturated with groups from a set of groups (X) over bar if any finite subgroup K of G is contained in a subgroup of G isomorphic to some group from (X) over bar. 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.