# A short note about diffuse Bieberbach groups

## TL;DR

This paper classifies low-dimensional diffuse Bieberbach groups up to dimension 6 and addresses a question about the minimal dimension of non-diffuse Bieberbach groups lacking a three-dimensional Hantzsche-Wendt subgroup.

## Contribution

It provides a complete classification of diffuse Bieberbach groups in dimensions up to 6 and answers an open question about their minimal non-diffuse counterparts.

## Key findings

- Classified diffuse Bieberbach groups up to dimension 6.
- Answered an open question on minimal dimension of certain non-diffuse Bieberbach groups.
- Identified properties related to the presence of Hantzsche-Wendt groups.

## Abstract

We consider low dimensional diffuse Bieberbach groups. In particular we classify diffuse Bieberbach groups up to dimension 6. We also answer a question from [S. Kionke, J. Raimbault, On geometric aspects of diffuse groups, Doc. Math. 21 (2016), page 887] about minimal dimension of a non-diffuse Bieberbach group which does not contain three-dimensional Hantzsche-Wendt group.