Finite Groups with Some SE-Supplemented Subgroups

Abstract EN

Let H be a subgroup of a finite group G, p a prime dividing the order of G, and P a Sylow p-subgroup of G for prime p.

We say that H is SE-supplemented in G if there is a subgroup K of G such that G=HK and H∩K≤HseG, where HseG denotes the subgroup of H generated by all those subgroups of H which are S-quasinormally embedded in G.

In this paper, we characterize p-nilpotency and supersolvability of G under the assumption that all maximal subgroups of P are SE-supplemented in NG(P).