# Products of two derangements in finite simple groups

- Reference: `kourovka-21-27-products-of-two-derangements-in-finite-simple-groups`
- Page: https://theoremdb.org/statements/kourovka-21-27-products-of-two-derangements-in-finite-simple-groups
- Record maturity: Reviewed problem

## Problem

A permutation on a set Ω is called a derangement if it has no fixed points in Ω. Let G be a finite simple transitive permutation group. Is it true that every element in G is the product of two derangements? This is Kourovka Notebook Problem \(21.27\).

## 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-21-27-products-of-two-derangements-in-finite-simple-groups`, 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.