Determine the exact number of subgroups of $\mathbb{Z}_{924}$ with addition
I know the group $(\mathbb{Z}_n, +)$ is cyclic. I realize how to find the number of elements of $\mathbb{Z}_{20}$ for say, but I am stuck on this. Can you help?
2025-01-13 02:40:18.1736736018
Determine the exact number of subgroups of $\mathbb{Z}_{924}$ with addition
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Under the canonical projection $\mathbb Z \to \mathbb Z_n$, the subgroups of $\mathbb Z_n$ correspond to the subgroups of $\mathbb Z$ containing $n\mathbb Z$ and these are of the form $d\mathbb Z$ where $d$ divides $n$.
Therefore, you only have to count the number of divisors of $924 = 2^2 \cdot 3 \cdot 7 \cdot 11$.