WEAKLY C-NORMAL AND Cs-NORMAL SUBGROUPS OF FINITE GROUPS

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 = HN , and H-N ≤ core_G H , where core_G core 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.