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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.

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- Thread starter Fairy111
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- #1

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

Some hints to how to do this would be great.

- #2

Dick

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What's (yxy^(-1))^n?

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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

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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