# Prove that if x = x^(-1) for all x in the group G, then G is abelian

• Mar 23rd 2010, 01:31 PM
rainyice
Prove that if x = x^(-1) for all x in the group G, then G is abelian
Prove that if x = x^(-1) for all x in the group G, then G is abelian.
• Mar 23rd 2010, 03:23 PM
tonio
Quote:

Originally Posted by rainyice
Prove that if x = x^(-1) for all x in the group G, then G is abelian.

For all $a,b\in G\,,\,\,ab=(ab)^{-1}$ ....develop this now.

Tonio
• Mar 23rd 2010, 07:59 PM
rainyice
Quote:

Originally Posted by tonio
For all $a,b\in G\,,\,\,ab=(ab)^{-1}$ ....develop this now.

Tonio

Thanks for the hint, but it wasn't helpful without explaination. But still thank you. Someone helped me through this problem already.