Title: On weakly s-normal subgroups of finite groups
Abstract: Assume that G is a finite group and H is a subgroup of G: We say that H is s-permutably imbedded in G if, for every prime number p that divides |H|; a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgroup of G; a subgroup H is s-semipermutable in G if HG p = G p H for any Sylow p-subgroup G p of G with (p, |H|) = 1; a subgroup H is weakly s-normal in G if there are a subnormal subgroup T of G and a subgroup H * of H such that G = HT and H∩T ≤ H *; where H * is a subgroup of H that is either s-permutably imbedded or s-semipermutable in G. We investigate the influence of weakly s-normal subgroups on the structure of finite groups. Some recent results are generalized and unified.