Über einen Algorithmus zur Bestimmung der Raumgruppen

  title={{\"U}ber einen Algorithmus zur Bestimmung der Raumgruppen},
  author={Hans J. Zassenhaus},
  journal={Commentarii Mathematici Helvetici},
  • H. Zassenhaus
  • Published 1 December 1948
  • Mathematics
  • Commentarii Mathematici Helvetici

Units in group rings of crystallographic groups

In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some

$$G_2$$-structures on flat solvmanifolds

  • Alejandro Tolcachier
  • Mathematics
    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
  • 2022
. In this article we study the relation between flat solvmanifolds and G 2 geometry. First, we give a classification of 7-dimensional flat splittable solvmanifolds using the classification of finite

A Users' Guide to Infra-nilmanifolds and Almost-Bieberbach groups

The aim of this text is to provide a clear description of the theory of Infra-nilmanifolds and their fundamental groups, the almost-Bieberbach groups. For most of the proofs of the results, we refer


A classical result by K. B. Lee states that every group morphism between almost crystallographic groups is induced by an affine map on the nilpotent Lie group whereon these groups by definition act.

Crystallographic Helly Groups

We prove that asymptotic cones of Helly groups are countably hyperconvex. We use this to show that virtually nilpotent Helly groups are virtually abelian and to characterize virtually abelian Helly

Unbounded domains in hierarchically hyperbolic groups

We investigate unbounded domains in hierarchically hyperbolic groups and obtain constraints on the possible hierarchical structures. Using these insights, we characterise the structures of virtually

Crystallographic actions on Lie groups and post-Lie algebra structures

  • D. Burde
  • Mathematics
    Communications in Mathematics
  • 2019
Abstract This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in 2017.

A-Foliations of codimension two on compact simply-connected manifolds

We show that a singular Riemannian foliation of codimension $2$ on a compact simply-connected Riemannian $(n + 2)$-manifold, with regular leaves homeomorphic to the $n$-torus, is given by a smooth