The Alperin Theorem for Periodic Groups with a Finite Sylow 2-Subgroup

We transfer the well-known Alperin theorem on fusion of the $ p $ -elements of Sylow $ p $ -subgroups of finite groups onto periodic groups with finite Sylow 2-subgroups for the case $ p=2 $ .The basis for this transfer is the famous Shunkov theoremon the local finiteness of a periodic group  $ G $ having an involution whose centralizer in $ G $ is finite.