# Concise words in residually finite groups

- Reference: `kourovka-21-105-concise-words-in-residually-finite-groups`
- Page: https://theoremdb.org/statements/kourovka-21-105-concise-words-in-residually-finite-groups
- Record maturity: Reviewed problem

## Problem

A group word w is said to be concise in a class C of groups if for every group G in C such that the set Gw of word values of w in G is finite, the verbal subgroup w(G) = ⟨Gw ⟩ is also finite (see also Archive 2.45). Is every word concise in the class of residually finite groups? See (D. Segal, Words. Notes on verbal width in groups, Cambridge Univ. Press, 2009) for a partial solution. This is Kourovka Notebook Problem \(21.105\).

## 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-21-105-concise-words-in-residually-finite-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.