# Math Help - Abelian Groups

1. ## 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.

2. 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.
$a(a^{-1}b^{-1})b = e(a^{-1}b^{-1})ba.$