On torsion images of Coxeter groups and question of Wiegold

TL;DR

This paper demonstrates that certain Coxeter groups can be mapped onto uncountably many infinite 2-groups with specific properties and affirms a question posed by Wiegold, expanding understanding of their torsion images.

Contribution

It shows that non-virtually abelian Coxeter groups with specific label conditions can be mapped onto many complex 2-groups and answers an open question by Wiegold.

Findings

Coxeter groups can map onto uncountably many infinite 2-groups

These 2-groups can be just-infinite and branch groups of intermediate growth

Affirmative answer to Wiegold's question in Kourovka Notebook

Abstract

We show that every Coxeter group that is not virtually abelian and for which all labels in the corresponding Coxeter graph are powers of 2 or infinity can be mapped onto uncountably many infinite 2-groups which, in addition, may be chosen to be just-infinite, branch groups of intermediate growth. Also we answer affirmatively a question raised by Wiegold in Kourovka Notebook.