Weakly c-normal and cs-normal subgroups of finite groups

Abstract EN

A subgroup H of a finite group G is weakly c—normal subgroup of G if there exists a subnormal subgroup N of G such that G = H, and H C \ N ≤ Core G (H), where Core G [H J denotes the core of H in G, which is the largest normal subgroup of G contained in H.

If H C^N ≤ CO re G [HJ, then H is cs—normal subgroup of G, where Core G (H) denotes the higher core of H in G, which is the largest subnormal subgroup of G contained in H.

In this paper, we investigate some properties of weakly c—normal and cs—normal subgroups of finite groups, and using the weakly c—normality and cs—normality of some Sylow and maximal subgroups to determine the structure of finite groups.