A note on the supersolubility of a group with ms-supersoluble factors

Abstract

A subgroup A of a group G is called seminormal in G, if there exists a subgroup B such that $G=AB$ and AX is a subgroup of G for every subgroup X of B. Let G be a supersoluble group. Then it has an ordered Sylow tower of supersoluble type $1=G_0< G_1< \cdots < G_m=G$. If for every i all maximal subgroups of $G_{i}/G_{i-1}$ are seminormal in $G/G_{i-1}$, then G is said to be ms-supersoluble. In this paper, we proved the supersolubility of a group $G=AB$ under condition that A and B are normal in G and ms-supersoluble.