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Math Help - Cyclic group as the Direct product

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    Cyclic group as the Direct product

    Prove that a cyclic group of order n can be written as the direct product of its subgroups if n is divisible by atleast 2 distinct primes.
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    Quote Originally Posted by Chandru1 View Post
    Prove that a cyclic group of order n can be written as the direct product of its subgroups if n is divisible by atleast 2 distinct primes.
    I am not sure what you mean be "direct product of its subgroups".
    If n=p_1^{a_1}\cdot ... \cdot p_k^{a_k} then \mathbb{Z}_n = \mathbb{Z}_{p_1^{a_1}}\times ... \times \mathbb{Z}_{p_k^{a_k}}
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