Anstract Algebra proof - cosets

1. Apr 27, 2009

kathrynag

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution
need to show gh1=h2g
I know I need to show this, but am unsure on how to.

2. Apr 27, 2009

kathrynag

I know the whole set up excpet for this part and it confuses me.

3. Apr 27, 2009

VKint

Let g be in G, h in H (sorry, Latex seems to be failing presently). As you say, you need to show that there exists k in H such that
gh = kg. You know that ghg-1 = k is in H. Rearrange this to get something useful.

4. Apr 28, 2009

kathrynag

Oh, that makes sense