Show that if H and K are normal subgroups of a group G such that H∩K = {e}, then hk = kh for all h ∈ H and for all k ∈ K.

This was in our study guide for the final and a couple friends of mine and I couldn't figure it out.

Printable View

- Dec 11th 2010, 07:48 AMDanielThriceNormal subgroups
Show that if H and K are normal subgroups of a group G such that H∩K = {e}, then hk = kh for all h ∈ H and for all k ∈ K.

This was in our study guide for the final and a couple friends of mine and I couldn't figure it out. - Dec 11th 2010, 08:06 AMOpalg
- Dec 11th 2010, 01:03 PMDanielThrice
So Essentially what we want to show is that hkh-1k-1=e.

But H∩K={e}, so we just have to show that hkh-1k-1∈ H and hkh-1k-1∈ K, but how do we do this? - Dec 11th 2010, 02:19 PMOpalg
- Dec 12th 2010, 07:48 AMDanielThrice
'm sorry I've tried a couple ways to solve it for K also but it's not working for this same set up

- Dec 12th 2010, 08:16 AMOpalg