Finite Groups With Some Weakly S-semipermutable Subgroups

A subgroup H of a nite group G is said to be S-semipermutable in G if for every Sylow subgroup Gp of G, which (jHj; p) = ۱, HGp = GpH. A subgroup H of G is said to be Weakly S-semipermutable in G if there exists normal subgroup T of G such that HT is S-permutable in G and H \ T is S-semipermutable in G. In this paper we prove that for a nite group G, if some subgroups of G with same order are Weakly S-semipermutable in G, then G is p-nilpotent.

Keywords:

S-permutable , S-semipermutable , Weakly S-semipermutable , p-nilpotentcy