Constructions of torsion-free countable, amenable, weakly mixing groups

TL;DR

This paper constructs specific torsion-free, countable, amenable, weakly mixing groups, addressing a question in the field and exploring related properties of verbal subgroups and crystallographic groups.

Contribution

It introduces the first known constructions of such groups, expanding understanding of their structure and properties.

Findings

Constructed torsion-free countable, amenable, weakly mixing groups

Answered a question posed by V. Bergelson

Presented results on verbal subgroups and crystallographic groups

Abstract

In this note, we construct torsion-free countable, amenable, weakly mixing groups, which answer a question of V. Bergelson. Some results related to verbal subgroups and crystallographic groups are also presented.