English

A Bieberbach theorem for crystallographic group extensions

Group Theory 2016-07-14 v1

Abstract

In this paper we prove that for each dimension nn there are only finitely many isomorphism classes of pairs of groups (Γ,N)(\Gamma,\mathrm{N}) such that Γ\Gamma is an nn-dimensional crystallographic group and N\mathrm{N} is a normal subgroup of Γ\Gamma such that Γ/N\Gamma/\mathrm{N} is a crystallographic group.

Keywords

Cite

@article{arxiv.1607.03503,
  title  = {A Bieberbach theorem for crystallographic group extensions},
  author = {John G. Ratcliffe and Steven T. Tschantz},
  journal= {arXiv preprint arXiv:1607.03503},
  year   = {2016}
}

Comments

18 pages. arXiv admin note: substantial text overlap with arXiv:1112.3981

R2 v1 2026-06-22T14:52:49.206Z