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In a group, show that ord(x) = ord(yxy^-1)

  1. May 8, 2009 #1
    1. The problem statement, all variables and given/known data

    If x and y are elements of a group G show that ord(x)=ord(yxy^-1)

    2. Relevant equations



    3. The attempt at a solution

    Some hints to how to do this would be great.
     
  2. jcsd
  3. May 8, 2009 #2

    Dick

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    Re: Groups

    What's (yxy^(-1))^n?
     
  4. May 9, 2009 #3
    Re: Groups

    y^n.x^n.y^(-n) ?
     
  5. May 9, 2009 #4

    Dick

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    Re: Groups

    You aren't going to get anywhere taking wild guesses. Try simplifying (yxy^(-1))^2=(yxy^(-1))(yxy^(-1)).
     
    Last edited: May 9, 2009
  6. May 9, 2009 #5
    Re: Groups

    that would be x^2
    so (yxy^(-1))^n would be x^n
     
  7. May 9, 2009 #6

    HallsofIvy

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    Re: Groups

    Yes, that is correct. Now, what does that have to do with the definition of "order"?

    Oops! Dick is correct. I forgot about the first and last y and y-1!

    But, "what does that have to do with the definition of 'order'" still stands.
     
    Last edited: May 9, 2009
  8. May 9, 2009 #7

    Dick

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    Re: Groups

    No. (yxy^(-1))^n would be yx^ny^(-1), NOT x^n. Be careful!!
     
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