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1 year ago
gh-37980: Fix order computation for linear groups GL(n, R) and SL(n, R) #36881 introduced some wrong results for orders of linear groups since it did not check whether the base ring is a field. We add the necessary checks as well as formulas for some further cases, namely $\mathbb{Z}$ and $\mathbb{Z}/q\mathbb{Z}.$ Finally, we add a `NotImplementedError` for the cases that are not supported. The formula for the general linear group over $\mathbb{Z}/q\mathbb{Z}$ is taken from https://math.stackexchange.com/a/2044571, and for the order of the special linear group we use the group isomorphism induced by the determinant. Fixes #37934. URL: https://github.com/sagemath/sage/pull/37980 Reported by: Sebastian A. Spindler Reviewer(s): Travis Scrimshaw
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