Suppose that $ M $ is some nonempty set of finite groups. A group $ G $ issaturated with groups from $ M $ if each finite subgroup of $ G $ liesin a subgroup isomorphic to an element of $ M $ .We prove that a periodic group with locally finite centralizers of involutionswhich is saturated with simple unitary groups of degree 4 over finite fields of fixed odd characteristic $ p $ is isomorphic to a simple unitary group of degree 4 over some locally finite field of characteristic $ p $ .
