THE INFLUENCE OF WEAKLY s-SUPPLEMENTED SUBGROUPS ON THE STRUCTURE OF FINITE GROUPS

Let G be a finite group. A subgroup H of G is said to be weakly s-supplemented in G if there exists a subgroup K of G such that G=HK and H KHsG, where H-sG is the subgroup of H generated by all those subgroups of H which are s-quasinormal in G. In this article, we investigate the structure of G under the assumption that some families of subgroups of G are weakly s-supplemented in G. Some recent results are generalized.