# Quotients of residually finite groups by amenable kernels

- Reference: `kourovka-21-118-quotients-of-residually-finite-groups-by-amenable-kernels`
- Page: https://theoremdb.org/statements/kourovka-21-118-quotients-of-residually-finite-groups-by-amenable-kernels
- Record maturity: Reviewed problem

## Problem

Is there any group which is not isomorphic to the quotient of a residually finite group by an amenable normal subgroup? This is Kourovka Notebook Problem \(21.118\).

## 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-21-118-quotients-of-residually-finite-groups-by-amenable-kernels`, 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.