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4
votes
3
answers
516
views
Finite subgroups of $O_n(\mathbb{Z})$ versus $O_n(\mathbb{Q})$
Are there any cases of finite subgroups of $O_n(\mathbb{Q})$ not contained in not isomorphic to any subgroup of $O_n(\mathbb{Z})$?
8
votes
3
answers
419
views
Does $O(4,\mathbb{Q})$ have an exceptional outer automorphism?
Does the orthogonal group $O(4,\mathbb{Q})$ have an exceptional outer automorphism analogous to that of its subgroup, the Coxeter/Weyl group $W(F_4)$?