Subgroups of locally finite productsof locally nilpotent groups

Abstract

Let the locally finite group G be the product of two locally nilpotent subgroups A and B, and assume that H is a subgroup of G belonging to a group classℱ . The question is considered whether there exists a subgroup X of G containing H which belongs to ℱ and satisfies . Under various assumptions on G and ℱ, necessary and sufficient conditions for the existence of such a subgroup X are obtained.