LAUSR

Let G be a finite group. A subgroup H of G is called an $${\mathcal{H}}$$H-subgroup in G if $${N_{G}(H)\cap H^{g} \leq H}$$NG(H)∩Hg≤H for all $${g\in G}$$g∈G. A subgroup H of G is called weakly c-supplemented in G if G has a subgroup K such that G = HK and $${ H\cap K}$$H∩K is an $${\mathcal{H}}$$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.