# Normal subgroup

1. Oct 1, 2008

### fk378

1. The problem statement, all variables and given/known data
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.

3. The attempt at a solution
How do i start this?

2. Oct 1, 2008

### morphism

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