About Periodic Groups of Shunkov Saturated by Central Expansions of Finite 2-Groups by Means of Group $L_2(5)$

Let $\Re$ be a set of finite groups. A group $G$ is said to be saturated by $\Re$, if every finite subgroup of $G$ is contained in a subgroup isomorphic to a group from $\Re$. We prove that a periodic group of Shunkov saturated by set $\Re=\{L_2(5)\times \langle v\rangle\}$, where $I_n$ — direct product of $n$ copys of groups of order 2, is locally finite group.