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Sums of quadratic forms over finite abelian groups
Let $A$ be a finite abelian group. Let $q:A\times A\to \mathbb{C}^{\times}$ be a non-degenerate bicharacter (that is: for every $a\in A$ $q(a,-)$ and $q(-,a)$ are characters of $A$, which are trivial ...
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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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