A short note about diffuse Bieberbach 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 [7, page 887] about the minimal dimension of a non-diffuse Bieberbach group which does not contain the three-dimensional Hantzsche-Wendt group.

Examples of non connective C *-algebras

“…A discrete group G is called locally indicable if every finitely generated non-trivial subgroup L of G has an infinite abelianization. The group G is called diffuse if every non-empty finite subset A of G has an element a ∈ A such that for any g ∈ G, either ga or g −1 a is not in A, see [6] and [7]. More examples of nonabelian connective groups were exhibited in [4], [5] and [6].…”