Proving Normal Subgroup of Abelian Groups

[fk378]

Homework Statement

Let G be a group and let H,K be subgroups of G.
Assume that H and K are Abelian. Let L=(H-union-K) be the subgroup of G generated by the set H-union-K. Show that H-intersect-K is a normal subgroup of L.

The Attempt at a Solution

How do i start this?

 

[morphism]

Start by understanding the definition of L. Then it should be pretty obvious that H$\cap$K is central in L.