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Rational linear groups with finitely many automorphism orbits
Show that a group of rational matrices with finitely many automorphism orbits is virtually soluble; check two proposed proofs.
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "algebra" |
| 5 | ], |
| 6 | "type": "proof", |
| 7 | "source": { |
| 8 | "key": "kourovka", |
| 9 | "name": "The Kourovka Notebook", |
| 10 | "url": "https://kourovkanotebookorg.wordpress.com/wp-content/uploads/2026/10/21tkt-3.pdf#page=184", |
| 11 | "id": "21.40", |
| 12 | "curator": "E. I. Khukhro and V. D. Mazurov", |
| 13 | "poser": "A. Dantas and E. de Melo", |
| 14 | "status": "unsolved; unverified AI solution proposed", |
| 15 | "as_of": "2026-10-20", |
| 16 | "catalog": "0521c19bbd38" |
| 17 | }, |
| 18 | "review": true, |
| 19 | "approval": "first-time" |
| 20 | } |