Multilinear commutators in residually finite groups

TL;DR

This paper proves that in residually finite groups, if products of a bounded number of multilinear commutator values have bounded order, then the associated verbal subgroup is locally finite.

Contribution

It establishes a new condition under which the verbal subgroup generated by multilinear commutators is locally finite in residually finite groups.

Findings

Verbal subgroup w(G) is locally finite under given conditions.

Bound on product length of w-values ensures local finiteness.

Results extend understanding of structure of residually finite groups.

Abstract

Let w be a multilinear commutator and n a positive integer. Suppose that G is a residually finite group in which every product of at most 896 w-values has order dividing n. Then the verbal subgroup w(G) is locally finite.