# Multilinear commutator values covered by cyclic subgroups

- Reference: `kourovka-21-98-multilinear-commutator-values-covered-by-cyclic-subgroups`
- Page: https://theoremdb.org/statements/kourovka-21-98-multilinear-commutator-values-covered-by-cyclic-subgroups
- Record maturity: Reviewed problem

## Problem

Let w be a multilinear commutator word, and assume that G is a group where the set of w-values is covered by finitely many cyclic subgroups. Is it true that the verbal subgroup w(G) is finite-by-cyclic? This is true for lower central words (G. Cutolo, C. Nicotera, J. Algebra, 324, no. 7 (2010), 1616-1624). This is Kourovka Notebook Problem \(21.98\).

## 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-21-98-multilinear-commutator-values-covered-by-cyclic-subgroups`, 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.