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How many subgroups of order $\prod_{1}^{n} p_{i}^{n_{i}}$ are there in the finite product of cyclic groups?
All of the following ${p_{i},q_{i}}$are prime numbers, ${n,m,k}$ are pre-assigned integers.
Consider the product of cyclic groups $\prod_{1}^{n} \mathbb Z_{p_{i}^{n_{i}}}$ then we asked the question:
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