A NOTE ON THE p-NILPOTENCY OF A FINITE GROUP

Abstract

Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing |H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-quasinormal in G. We investigate the influence of s-quasinormally embedded and weakly s-supplemented subgroups on the p-nilpotency of a finite group.