Originally Posted by
xoyankeegirlx3 Show that if H,K are normal to G and H intersect K = {1}, then hk=kh for all h in H, and k in K.
I have tried playing around with this for a long time. I just can't quite get it right. I've used the facts of the normal subgroup tests, gHg^-1 in H and gKg^-1 in K, the fact that gH=Hg and gK=Kg. I've tried using kHk^-1 in H and hKh^-1 in K. I just can't quite get it to work. All I am able to achieve is getting hk=k2h and kh=h2k...
Any tips would be greatly appreciated!!! I have tried searching around a bit and can't find anything.