The Relation between c-normal Subgroups and Weakly c-normal Subgroups

A group H of G is called c-normal in G if there exists a normal subgroup K of G such that G=HK and H∩K≤HG where HG=∩g∈GHg is the maximal normal subgroup of G that is contained in H.A subgroup H of G is called weakly c-normal in G if there exists a subnormal subgroup K of G such that G=HK and H∩K≤HG.It is easy to see from the definition that a c-normal subgroup must be weakly c-normality,but the converse don't hold.Some equivalent conditions between c-normality and weakly c-normality were obtaine...