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Math Help - Need help with showing that orders of elements are equal...

  1. #1
    Junior Member ginafara's Avatar
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    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!!!
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  2. #2
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    Quote Originally Posted by ginafara View Post
    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 \mbox{ord}(b) = n. Then (aba^{-1})^n = ab^na^{-1} = aea^{-1} = e. Now argue that n is the smallest exponent for aba^{-1}.
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