ON THE p-NILPOTENCE OF FINITE GROUPS

In this paper, we give a new definition-a CSS subgroup(a subgroup H of a finite group G is called a CSS-subgroup of G if there exists a normal subgroup K of G such that G = HK and H boolean AND K is SS-quasinormal in G). By this definition, we investigate the relationship between the p-nilpotence of G and the p-nilpotence of N-G(P), and generalize the corresponding results to a saturated formation which contains the class N-p of all p-nilpotent groups, where p is an odd prime factor of vertical bar C vertical bar, P a Sylow p-subgroup of a group G.