Anstract Algebra proof - cosets

[kathrynag]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

need to show gh1=h2g
I know I need to show this, but am unsure on how to.

 

[kathrynag]

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

 

[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.

 

[kathrynag]

Oh, that makes sense