ON THE p-NILPOTENCE OF FINITE GROUPS

Abstract

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 ∩ 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 \(\mathcal{F}\) which contains the class \(\mathcal{N}_p\) of all p-nilpotent groups, where p is an odd prime factor of |G|, P a Sylow p-subgroup of a group G.