Let n greater than or equal to 2 and let k1,...,kn be positive integers. Recall that...

Let n greater than or equal to 2 and let k1,...,kn be positive integers. Recall that Ck1,..., Ckn denote the cyclic groups of order k1,...,kn. Prove by induction that their direct product Ck1×Ck2×....×Ckn is cyclic if and only if the ki's are pairwise coprime which means gcd(ki,kj)=1 for every i not equals j in {1,...n}.

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Colby Messinger answered 2 years ago

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