Q -permutable subgroups of finite groups - Miao, L.; Pu, Zh. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
A subgroup H of a group G is called Q-permutable in G if there exists a subgroup B of G such that (1) G = HB and (2) if H_1 is a maximal subgroup of H containing H_QG, then H_1B = BH_1 < G, where H_QG is the largest permutable subgroup of G contained in H. In this paper we prove that: Let F be a saturated formation containing U and G be a group with a normal subgroup H such that G/H F. If every maximal subgroup of every noncyclic Sylow subgroup of F∗(H) having no supersolvable supplement in G is Q-permutable in G, then G F.