# Abelian group

• Aug 6th 2007, 07:00 PM
r7iris
Abelian group
Let G be a group in which a^2=e (the id.) for all elements a of G. Show that G is Abelian.
• Aug 6th 2007, 08:19 PM
ThePerfectHacker
Quote:

Originally Posted by r7iris
Let G be a group in which a^2=e (the id.) for all elements a of G. Show that G is Abelian.

$(ab)^2 = e$
Expand,
$abab=e$
So,
$ab=ba$ (since $a^{-1} = a \mbox{ and }b^{-1}=b$).