A **split Cartan subgroup** of $\GL_2(\F_p)$ is a Cartan subgroup that is diagonalizable over $\F_p$. Every split Cartan subgroup is conjugate to the subgroup of diagonal matrices, which is isomorphic to $\F_p^\times\times\F_p^\times$.

The label **Cs** identifies the split Cartan subgroup of diagonal matrices.

The label **Cs.a.b** identifies the proper subgroup of **Cs** generated by
\[
\begin{pmatrix}a&0\\0&1/a\end{pmatrix}, \begin{pmatrix}b&0\\0&r/b\end{pmatrix},
\]
where $a$ and $b$ are minimally chosen positive integers and $r$ is the least positive integer generating $(\Z/p\Z)^\times\simeq \F_p^\times$, as defined in [arXiv:1504.07618, 10.1017/fms.2015.33, MR:3482279].

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- Review status: beta
- Last edited by Andrew Sutherland on 2021-09-18 14:52:28

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- 2021-09-18 14:52:28 by Andrew Sutherland
- 2021-09-18 09:49:25 by Andrew Sutherland
- 2021-09-18 09:43:34 by Andrew Sutherland
- 2017-03-16 14:00:14 by Andrew Sutherland

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