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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- Sep 25th 2008, 05:00 PMJCIRAbelian 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. - Sep 25th 2008, 05:34 PMNonCommAlg