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Math Help - Prove Cyclic

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    Prove Cyclic

    Suppose that G is Abelian group of order 35 and every element of G satisfies the equation x^35=e. Prove that G is cyclic
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    Quote Originally Posted by mandy123 View Post
    Suppose that G is Abelian group of order 35 and every element of G satisfies the equation x^35=e. Prove that G is cyclic
    The condition x^{35} = e is absolutely unnecessary because that is just Lagrange's theorem.
    Since 35 = 5\cdot 7 for two distinct primes it means that is must be cyclic.
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