Weakly c-permutable subgroups of finite groups

A subgroup H of a group G is called weakly c-permutable in G if there exists a subgroup T of G such that G=HT and H∩T is completely c-permutable in G. In this paper, we obtain some results about the weakly c-permutable subgroups and use them to determine the structures of some groups. In particular, we give some new characterizations of supersolvability and p-nilpotency of a group (and, more general, a group belonging to a given formation of finite groups) by using the weakly c-permutability of some primary subgroups. As application, we generalize a series of known results.