On weakly s-permutably embedded subgroups of finite groups (II)

Suppose that G is a finite group and H is a subgroup of G. H is said to be s-permutably embedded in G if for each prime p dividing |H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-permutable subgroup of G; H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup Hse of G contained in H such that G = HT and H ∩ T ⩽ Hse. In this paper, we continue the work of [Comm. Algebra, 2009, 37: 1086–1097] to study the influence of the weakly s-permutably embedded subgroups on the structure of finite groups, and we extend some recent results.