Is there a classification of finite subgroups of $SL_2({\mathbb R})\times SL_2({{\mathbb R}})$?
For instance we have all cyclic groups and all direct products of two cyclic groups. Are there any others?
2025-01-13 05:23:06.1736745786
Finite subgroups of $SL_2({\mathbb R})\times SL_2({{\mathbb R}})$
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Every finite subgroup lies in a maximal compact subgroup, so it amounts to classify finite subgroups of the torus $(\mathbf{R}/\mathbf{Z})^2$, and hence of its torsion subgroup $(\mathbf{Q}/\mathbf{Z})^2$. In conclusion, up to isomorphism we precisely get all direct products of two finite cyclic groups.