Let H and K be normal subgroups of G such that H intersect K=<e>. Show that hk=kh for all h in H and k in K.

H and K are normal so ghg^-1 is in H and gkg^-1 is in K.

want to show hk=kh. So basically I'm showing this is abelian.

Can I do ghg^-1=gkg^-1?

ghg^-1g=gkg^-1g

gh=gk

so that works if g=h