Thread: 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.

Originally Posted by JCIR

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.