# Commutator values in finite groups

- Reference: `kourovka-21-35-commutator-values-in-finite-groups`
- Page: https://theoremdb.org/statements/kourovka-21-35-commutator-values-in-finite-groups
- Record maturity: Reviewed problem

## Problem

Let G be a finite group, w a multilinear commutator group-word, and p a prime. Suppose that p divides the order |xy| whenever x is a w-value of p′ -order in G and y is a w-value in G of order divisible by p. Is it true that then the verbal subgroup w(G) must be p-nilpotent? Without the assumption that w be multilinear, the answer is negative. An affirmative answer has been obtained in several special cases (J. Algebra, 609 (2022), 926-936). This is Kourovka Notebook Problem \(21.35\).

## Status

The reviewed record remains open.

## Work

### Working on this

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## References

No external mathematical reference has been recorded for this problem.