On Weakly ss-Supplemented Subgroups of Finite Groups

Let H be a subgroup of a finite group G. We say that H is weakly ss-supplemented in G if there exists a subgroup T of G and an s-semipermutable subgroup Hss of G contained in H such that G = HT and H∩T ≤ Hss. In this paper, we get some new characterizations of supersolvability and nilpotentcy of G by assuming some minimal subgroups of G are weakly ss-supplemented. Some recent results are extended and generalized.