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Math Help - Coset proof

  1. #1
    Senior Member sfspitfire23's Avatar
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    Coset proof

    I'm having some trouble figuring out this proof:

    Let H be a subgroup of G and suppose that Ha=bH for a,b in G. Show aH=Hb.

    Any suggestions?
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  2. #2
    MHF Contributor
    Opalg's Avatar
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    Re: Coset proof

    Quote Originally Posted by sfspitfire23 View Post
    I'm having some trouble figuring out this proof:

    Let H be a subgroup of G and suppose that Ha=bH for a,b in G. Show aH=Hb.

    Any suggestions?
    If e is the identity of G then a = ea \in Ha. Therefore a = bh for some h\in H. So aH = bhH = bH = Ha, and similarly Hb = bH.
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