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    Question prove

    prove that if the order of group G is a prime number then G is cyclic.
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  2. #2
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    Quote Originally Posted by mandy123 View Post
    prove that if the order of group G is a prime number then G is cyclic.
    Let  a\in G - \{ e \} then \text{ord}(a) > 1 and \text{ord}(a) divides p by Lagrange's theorem.
    Therefore, \text{ord}(a) = p since p is a prime. Therefore \left< a \right> = G.
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