# Irreducible algebraic-group actions in finite Morley rank

- Reference: `kourovka-21-21-irreducible-algebraic-group-actions-in-finite-morley-rank`
- Page: https://theoremdb.org/statements/kourovka-21-21-irreducible-algebraic-group-actions-in-finite-morley-rank
- Record maturity: Reviewed problem

## Problem

Prove that a simple (that is, without proper non-trivial connected normal subgroups) algebraic group M over an algebraically closed field cannot act definably, faithfully, and irreducibly on a simple group of finite Morley rank other than M/Z(M ). This is Kourovka Notebook Problem \(21.21\).

## 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-21-21-irreducible-algebraic-group-actions-in-finite-morley-rank`, 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.