On Groups with Finite Abelian Section Rank Factorized by Mutually Permutable Subgroups

Abstract

It is proved that if G = AB is a soluble group with finite abelian section rank which is factorized by two mutually permutable finite-by-nilpotent subgroups A and B such that A′ and B′ are locally nilpotent, then also the normal closure ⟨ A′, B′ ⟩G is locally nilpotent and the subgroups A′ and B′ are ascendant in G.