Thread: 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!!!

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 . Then . Now argue that is the smallest exponent for .