# Stabilizer subgroups - proof verification

• Nov 8th 2013, 05:18 PM
abscissa
Stabilizer subgroups - proof verification
I have a problem that I would like help on. I'm preparing for an exam, and I have provided my work below.

Problem statement: Let G act on X, and suppose x,y in X are in the same orbit for this action. How are the stabilizer subgroups G_x and G_y related?

My attempt:G_x = G_y = {g in G: gx=x} = {g in G: gy=y} for all x,y in X, for all g in G.

Thanks.
• Nov 26th 2013, 09:50 PM
Haven
Re: Stabilizer subgroups - proof verification
The answer is $G_y = hG_x h^{-1}$ for some $h\in G$.

See if you can derive it.