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Math Help - cosets-group-subgroup

  1. #1
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    cosets-group-subgroup

    we are given H is a subgroup of G and whenever have Ha not equal to Hb...then aH is not equal to bH.....we have to prove that g.H.(g^-1) is a subset of H...thnx in advance...
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by prashantgolu View Post
    we are given H is a subgroup of G and whenever have Ha not equal to Hb...then aH is not equal to bH.....we have to prove that g.H.(g^-1) is a subset of H...thnx in advance...
    Firstly, you should prove that left and right cosets coincide precisely (you will need to use your assumption to prove this). That is, for all gH \in G/H there exists an h \in  G such that gH=Hh. How does this help you? (You will need a second application of your assumption here.)
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