I am reading a set of notes (on modular curves: here), which seems to suggest on page 5 that $\frac{1}{11}\mathbb{Z}$ is a cyclic group of order 11. Am I missing something? Doesn't this notation just mean the integers multiplied by $11$, which certainly doesn't have order 11?
2026-04-02 03:19:39.1775099979
Meaning of notation $\frac{1}{N}\mathbb{Z}$
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It is of course the rational numbers whose denominator is $11$. Its image in the complex torus $\Bbb{C/(Z+\tau Z)}$ is a cyclic subgroup with $11$ elements.