C-normality of groups and its properties

A subgroup H is called c-normal in group G if there exists a normal subgroup N of G such that HN = G and H boolean AND N less than or equal to H-G, where H-G = Core(H) = boolean AND(g is an element of G)H(g) is the maximal normal subgroup of G which is contained in H. We obtain some results about the c-normal subgroups and use them to determine the structures of some groups. (C) 1996 Academic Press, Inc.