On Finite Groups Factorised by Submodular Subgroups

Abstract

A subgroup H of a finite group G is submodular in G if there is a subgroup chain \(H=H_0\le \ldots \le H_i\le H_{i+1}\le \ldots \le H_n=G\) such that \(H_i\) is a modular subgroup of \(H_{i+1}\) for every i. We investigate finite factorised groups with submodular primary (cyclic primary) subgroups in factors. We indicate a general approach to the description of finite groups factorised by supersolvable submodular subgroups.