Finite groups with certain kind of subgroups weakly c-supplemented

Abstract

Let G be a finite group. A subgroup H of G is called an \({\mathcal{H}}\)-subgroup in G if \({N_{G}(H)\cap H^{g} \leq H}\) for all \({g\in G}\). A subgroup H of G is called weakly c-supplemented in G if G has a subgroup K such that G = HK and \({ H\cap K}\) is an \({\mathcal{H}}\)-subgroup in G. We investigate the structure of finite groups by means of weakly c-supplemented subgroups. Some recent results about supersolvability of finite groups are generalized to a saturated formation containing the class of all supersolvable groups.