FINITE GROUPS WITH SOME WEAKLY S-SUPPLEMENTED SUBGROUPS.

Let H be a subgroup of a group G. Then, we call H weakly s-supplemented in G if G has a subgroup T such that HT = G and H ∩ T ≤ HsG, where HsG is the largest s-permutable subgroup of G contained in H. In this paper, we use the weakly s-supplemented subgroups to characterize the structure of groups. A series of known results in the literature are unified and generalized. [ABSTRACT FROM PUBLISHER]