On s-Semiembedded Subgroups of Finite Groups

Abstract

Suppose that G is a finite group and H is a subgroup of G. We say that H is s-semipermutable in G if HGp = GpH for any Sylow p-subgroup Gp of G with (p, |H|) = 1; H is s-semiembedded in G if there is a normal subgroup T of G such that HT is s-semipermutable in G and H ∩ T ≤ HssG, where HssG is the subgroup of H generated by all those subgroups of H which are s-semipermutable in G. We investigate the influence of s-semiembedded subgroups on the structure of finite groups. Some recent results are generalized and unified.