The influence of weakly s-permutably embedded subgroups on the p-nilpotency of finite groups

Suppose G is a finite group and H is a subgroup of G.H is said to be s-permutably embedded in G if for each prime p- dividing vertical bar H vertical bar, a Sylow p-subgroup of H is also a Sylowp-subgroup of somes-permutable subgroup of G; H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of Gandan s-permutably embedded subgroup H-se of G contained in H such that G=HT and H boolean AND T <= H-se. We investigate the influence of weakly s-permutably embedded subgroups on the p-nilpotency of finite groups.