On weakly s -normal subgroups of finite groups - Li, Yangming; Qiao, Shouhong (Ukrains’kyi Matematychnyi Zhurnal, 2011)
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_pH 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.