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

  • Thread starter Fairy111
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  • #1
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Homework Statement



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

Homework Equations





The Attempt at a Solution



Some hints to how to do this would be great.
 

Answers and Replies

  • #2
Dick
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What's (yxy^(-1))^n?
 
  • #3
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y^n.x^n.y^(-n) ?
 
  • #4
Dick
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y^n.x^n.y^(-n) ?

You aren't going to get anywhere taking wild guesses. Try simplifying (yxy^(-1))^2=(yxy^(-1))(yxy^(-1)).
 
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  • #5
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that would be x^2
so (yxy^(-1))^n would be x^n
 
  • #6
HallsofIvy
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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.
 
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  • #7
Dick
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that would be x^2
so (yxy^(-1))^n would be x^n

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

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