Characterizing finite groups with mutually N-permutable products and smooth maximal subgroups

Abstract

Let G = HK be a finite group, where H and K are proper subgroups of G. A group G is called a mutually N-permutable product of H and K if H permutes with every normal subgroup of K, and K permutes with every normal subgroup of H. In this paper, as a next step of some recently studies, we examine the structural properties of finite group G that is a mutually N-permutable product of two subgroups, with the additional assumption that all maximal subgroups of G are generalized smooth groups.