C-normality and solvability of groups Original Research Article

A subgroup H is called c-normal in group G if there exists a normal subgroup N and G such that HN = G and H ∩ N ≤ HG where HG =: Core(H) = square cupgset membership, variantG Hg is the maximal normal subgroup of G which is contained in H. We obtain some results about the c-normal subgroups and the solvability of groups.