I need to prove:
So, one direction is quite easy:
If is a subgroup of , it follows that : .
in particular, for every , , so , .
but the second direction is not quite clear for me:
Since , : , there exist some , such that
but how do I know that ?
Thanks in advance.
thanks for the help.
scrap that last post.
I got it.
for some reason I thought that every normal subgroup is abelian...