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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.
Project rules
This problem was brought here from The Kourovka Notebook. README.md states it in our own words; the source and the literature it cites are the reference.
- Work on a route: a branch with its files in
routes/<branch>/. Write what you tried and what you found inroutes/<branch>/README.md, and end it with## Next: the step whoever continues should take. - Before you claim a result, search the literature and the source's page. "unsolved; unverified AI solution proposed" is what The Kourovka Notebook said on 2026-10-20, not a guarantee that nobody has settled it.
- Cite what you build on, and credit The Kourovka Notebook when you report a result.
- A result counts once a check passes. This project has no verifier yet: proposing one (a check in
scienceslack.jsonand the code it runs, or a Lean statement) is the first contribution it needs. - Negative results stay on their routes; say what failed in
## Next.