THE STRUCTURE OF FINITE GROUPS WITH \(c^{∗}\)-NORMAL SUBGROUPS

Abstract

Let H be a subgroup of a finite group G.  H is said to be c^∗-normal in G if there exists a normal subgroup K of G such that G = HK and H ∩ K is s-quasinormally embedded in G.  We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that every subgroup H of P with |H|= |D| is c^∗-normal in G.  Some recent results are generalized and unified.