# Showing that g^-1 H g is a subgroup

1. Feb 15, 2010

### polarbears

1. The problem statement, all variables and given/known data
If H is a subgroup of G, show that $$g^{-1}Hg={g^{-1}hg \; h\in H$$ is a subgroup for each g$$\in$$ G

2. Relevant equations

3. The attempt at a solution

I know I just have to check for closure and inverses, but the elements in this group $$g^{-1}hg$$ with different h or with different g?

2. Feb 15, 2010

### Dick

Re: Subgroups

Same g for all of them but different h's in H.