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Math Help - Abelian Groups

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    Abelian Groups

    Suppose that G is a group with the property that for every choice of elements in G, axb=cxd implies ab=cd. Prove that G is abelian.
    "Middle cancelation" implies commutativity.
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    Quote Originally Posted by JCIR View Post
    Suppose that G is a group with the property that for every choice of elements in G, axb=cxd implies ab=cd. Prove that G is abelian.
    "Middle cancelation" implies commutativity.
    a(a^{-1}b^{-1})b = e(a^{-1}b^{-1})ba.
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