The **level** of an open subgroup $H$ of a matrix group $G$ over $\widehat \Z$ is the least positive integer $N$ for which $H$ is equal to the inverse image of its projection to the reduction of $G$ modulo $N$.

This also applies to open subgroups of matrix groups over $\Z_\ell$, in which case the level is necessarily a power of $\ell$.

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**Knowl status:**

- Review status: beta
- Last edited by Andrew Sutherland on 2021-09-18 14:41:43

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**History:**(expand/hide all)

- 2021-09-18 14:41:43 by Andrew Sutherland
- 2021-09-18 09:50:40 by Andrew Sutherland
- 2021-07-17 11:30:07 by Andrew Sutherland
- 2021-07-17 11:29:06 by Andrew Sutherland
- 2021-07-17 11:26:28 by Andrew Sutherland

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