# Minimal topological groups and semidirect products

- Reference: `kourovka-21-103-minimal-topological-groups-and-semidirect-products`
- Page: https://theoremdb.org/statements/kourovka-21-103-minimal-topological-groups-and-semidirect-products
- Record maturity: Reviewed problem

## Problem

A Hausdorff topological group G is called minimal if it does not admit a strictly coarser Hausdorff group topology. A topological group is called Raikov complete if its two-sided uniform structure is complete. It is known that a finite direct product of Raikov complete minimal topological groups is again minimal. Is it true that an arbitrary Cartesian product of Raikov complete minimal topological groups remains minimal? It is known that an arbitrary Cartesian product of centre-free minimal topological groups is minimal (M. Megrelishvili, Topology Appl., 62, no. 1 (1995), 1-19). This is Kourovka Notebook Problem \(21.103\).

## 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-21-103-minimal-topological-groups-and-semidirect-products`, 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.