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Thread: Prove not cyclic

  1. #1
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    Prove not cyclic

    Let p and q be odd primes and let m and n be positive integers. Prove that U(p^m) + U(a^n) is not cyclic.
    (+ is the external direct product (+ with a circle around it))
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    Quote Originally Posted by mandy123 View Post
    Let p and q be odd primes and let m and n be positive integers. Prove that U(p^m) + U(a^n) is not cyclic.
    (+ is the external direct product (+ with a circle around it))
    I think you mean to say U(p^m) \times U(q^n). Since p,q are odd it means 2 divides both |U(p^m)|,|U(q^m)|. And therefore \gcd( |U(p^m)|,|U(q^m)|) \not = 1. Thus, their product cannot be cyclic.
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