Chapter 15.1 Introduction and definitions

Space‐group symmetry

First Online Edition (2006)

Part 15. Normalizers of space groups and their use in crystallography

  1. E. Koch1,
  2. W. Fischer1,
  3. U. Müller2

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000533

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Koch, E., Fischer, W. and Müller, U. 2006. Introduction and definitions. International Tables for Crystallography. A:15:15.1:878.

Author Information

  1. 1

    Institut für Mineralogie, Petrologie und Kristallographie, Philipps‐Universität, D‐35032 Marburg, Germany

  2. 2

    Fachbereich Chemie, Philipps‐Universität, D‐35032 Marburg, Germany

Publication History

  1. Published Online: 1 JAN 2006



In Chapter 15.1, the mathematical concept of Euclidean and affine normalizers of space groups is introduced. Some crystallographic problems are mentioned for which the solution of the problem is simplified by the use of normalizers.


  • normalizers;
  • space groups;
  • Euclidean normalizers;
  • affine normalizers;
  • Cheshire groups