# Orderings of Witzel-Zaremsky-Thompson groups

## TL;DR

This paper proves that the Witzel-Zaremsky-Thompson group is orderable when constructed from a compatible direct system of orderable groups, expanding understanding of group orderability properties.

## Contribution

It establishes the orderability of the Witzel-Zaremsky-Thompson group under specific conditions, a new result in the study of these groups.

## Key findings

- Witzel-Zaremsky-Thompson group is orderable under certain conditions
- Orderability depends on compatibility of the direct system of groups
- Advances understanding of algebraic properties of complex groups

## Abstract

We prove the orderability of the Witzel-Zaremsky-Thompson group for a direct system of orderable groups under a certain compatibility assumption.