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Math Help - L has a unique subfield K. Prove u^h is in K.

  1. #1
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    L has a unique subfield K. Prove u^h is in K.

    Let p be a prime, and let m and n be positive integers such that m divides n. Let h be a positive integer as well. Let L be a field of order p^n, and let u be an element of L. L has a unique subfield K of order p^m.

    Prove that u^h is in K.

    Any help please?
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  2. #2
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    Re: L has a unique subfield K. Prove u^h is in K.

    i think you need more conditions on h. after all, 1 is a positive integer, and if u is in K (for any element u of L), then we get m = n.
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