Weakly c-Normal and cs-Normal Subgroups of Finite Groups

Abstract

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 N , and H∩N ≤ core_G (H), where core_G (H) denotes the core of H in G, which is the largest normal subgroup of G contained in H. If H∩N ≤ core_G.. (H), then H is c_s − 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 c_s − normal subgroups of finite groups, and using the weakly c − normality and c_s − normality of some Sylow and maximal subgroups to determine the structure of finite groups.

Keywords: Normality, Weakly c − normal, c_s − normal, Sylow and maximal subgroups.

2000 Mathematics Subject Classification. Primary: 20D35 , Secondary: 20E15; 20F22