maybe i'm just really bad at math, but... isn't this question in the wrong forum area?? just a though. After all.. it is abstract algebra, and i think MHF has a different forum section for those types of questions.
Let H be a subgroup of G such that g^-1hg is an element of H for all g in G and all h in H. Show that every left coset gH is the same as the right coset Hg.
need to show gh1=h2g
I know I need to show this, but am unsure on how to.
I know the whole set up excpet for this part and it confuses me.
I'm a little rusty on the group theory stuf but I can recall the following:
Every subgroup of an abelian group is normal. As your subgroup H is normal as maybe we can assume G is abelian (help anyone!)
So if you can prove that G is in fact abelian then the following should follow for your cosets
if then
operating on cosets
I hope this helps some.