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Math Help - cosets

  1. #1
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    cosets

    Could someone help me with this proof? Thanks!

    Let G be a group, and H a subgroup of G.
    Ha = Hb iff ab^-1 is in H
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  2. #2
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    Quote Originally Posted by chris27 View Post
    Could someone help me with this proof? Thanks!

    Let G be a group, and H a subgroup of G.
    Ha = Hb iff ab^-1 is in H
    Ha = Hb \Leftrightarrow Hab^{-1} = Hbb^{-1} \Leftrightarrow Hab^{-1} = He \Leftrightarrow Hab^{-1} = H \Leftrightarrow ab^{-1} \in H.
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  3. #3
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    I do not like your proof Soltras.

    Ha = Hb now a\in Ha so a\in Hb that means a=hb for some ab^{-1} = h \in H. The converse if almost identity.
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