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Math Help - abstract algebra

  1. #1
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    abstract algebra

    a, b are in G, a group. H is a subgroup. If aH = bH then Ha^(-1) = Hb^(-1). Prove/disprove.

    I can't even tell if this is true or false so I really can't prove it!
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  2. #2
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    Quote Originally Posted by fulltwist8 View Post
    a, b are in G, a group. H is a subgroup. If aH = bH then Ha^(-1) = Hb^(-1). Prove/disprove.

    I can't even tell if this is true or false so I really can't prove it!
    Hint: xH = yH if and only if x^{-1}y \in H and same situation with Hx=Hy.
    Last edited by ThePerfectHacker; February 27th 2008 at 07:25 PM.
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  3. #3
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    Quote Originally Posted by ThePerfectHacker View Post
    Hint: xH = yH if and only if xy^{-1} \in H
    xH = yH\ \Leftrightarrow\ \color{red}y^{-1}x\color{black}\in H
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  4. #4
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    Quote Originally Posted by JaneBennet View Post
    xH = yH\ \Leftrightarrow\ \color{red}y^{-1}x\color{black}\in H
    It makes no difference. Because if y^{-1} x\in H then (y^{-1} x)^{-1} = x^{-1}y\in H.

    EDIT: Okay, I see I wrote it the other way around.
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  5. #5
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    ok thanks, i figured that out!!... but what about if it's "If aH = bH, then a^2 H = b^2 H"?
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