Finite groups with some weakly s-supplementally embedded subgroups

A subgroup H of G is said to be weakly s-supplementally embedded in G if there exist a subgroup T of G and an s-permutably embedded subgroup H_{se} of G contained in H such that G=HT and H cap T leq H_{se}. In this paper, we investigate the influence of some weakly s-supplementally embedded subgroups on the structure of a finite group G. Some earlier results are unified and generalized.