On the Finite Group Which Is a Product of Two Subnormal Supersolvable Subgroups

Abstract

Let G be a finite group that is a product of two subnormal ( normal) supersolvable subgroups. The following are interesting topics in the study of the structure of G: obtaining the conditions in addition to guarantee that G is supersolvable and giving the detailed structure of G when G is non-supersolvable. In this paper, we obtain a characteristic property of G being non-supersolvable and two new sufficient conditions for G being a supersolvable group.