On the supersolubility of a finite group with NS-supplemented subgroups

Abstract

A subgroup A of a group G is said to be NS-supplemented in G, if there exists a subgroup B of G such that G = AB and whenever X is a normal subgroup of A and p ∈ π(B), there exists a Sylow p-subgroup B p of B such that XB p = B p X. In this paper, we proved the supersolubility of a group with NS-supplemented non-cyclic Sylow subgroups. The solubility of a group with NS-supplemented maximal subgroups is obtained.