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Math Help - Stabilizer subgroups - proof verification

  1. #1
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    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.
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  2. #2
    Member Haven's Avatar
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    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.
    Thanks from topsquark
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