# Need help with showing that orders of elements are equal...

• Oct 8th 2007, 05:11 PM
ginafara
Need help with showing that orders of elements are equal...
I need some help from some of the algebraists on the board.

I have the following problem... I have tried so many ways to prove it but I just can't seem to get there.

The Problem is:

Let G be a group with a,b in G. Prove that b and aba^(-1) have the same order.

I have attempted to show for finite order and infinite order, but no matter what i do I can't see it... Any help would be greatly appreciated...

Thanks!!!
• Oct 8th 2007, 05:13 PM
ThePerfectHacker
Quote:

Originally Posted by ginafara
I need some help from some of the algebraists on the board.

I have the following problem... I have tried so many ways to prove it but I just can't seem to get there.

The Problem is:

Let G be a group with a,b in G. Prove that b and aba^(-1) have the same order.

Say \$\displaystyle \mbox{ord}(b) = n\$. Then \$\displaystyle (aba^{-1})^n = ab^na^{-1} = aea^{-1} = e\$. Now argue that \$\displaystyle n\$ is the smallest exponent for \$\displaystyle aba^{-1}\$.