On s-semipermu table and c-normal subgroups of finite groups

Abstract EN

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 c-normal in G if G has a normal subgroup T suchth that G = HT and H ∩ T ≤ HG, where HG is the normal core of H in G.

We fix in every non-cyclic Sylow subgroup P of G some subgroup Dsatisfying 1 < |D| < |P| and study the structure of G under the assumption that every subgroup H of P with |H| = |D| is either s-semipermutable or c-normal in G.

Some recent results are generalized and unified.