C-supplemented subgroups of finite groups

A subgroup H of a group G is said to be c-supplemented in G if there exists a subgroup K of G such that HK = G and H boolean AND K is contained in Core(G)(H). We follow Hall's ideas to characterize the structure of the finite groups in which every subgroup is c-supplemented. Properties of c-supplemented subgroups are also applied to determine the structure of some finite groups.