# Linear groups with finitely many automorphism orbits

- Reference: `kourovka-21-40-linear-groups-with-finitely-many-automorphism-orbits`
- Page: https://theoremdb.org/statements/kourovka-21-40-linear-groups-with-finitely-many-automorphism-orbits
- Record maturity: Reviewed problem

## Problem

Let G be a subgroup of GL(n, Q) with finitely many orbits under automorphisms. Is G a virtually soluble group? This is Kourovka Notebook Problem \(21.40\).

## Status

The reviewed record remains open.

## Work

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `kourovka-21-40-linear-groups-with-finitely-many-automorphism-orbits`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.