Index

Müller, U.

doi:10.1107/97809553602060000547

International
Tables for
Crystallography
Volume A1
Symmetry relations between space groups
Edited by Hans Wondratschek and Ulrich Müller

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International Tables for Crystallography (2006). Vol. A1. ch. 3.1, p. 429 | 1 | 2 |

Section 3.1.1.6.1. Index

Ulrich Müller^a ^*

^a Fachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany
Correspondence e-mail: mueller@chemie.uni-marburg.de

3.1.1.6.1. Index

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The entry for every subgroup begins with the index in brackets, for example [2] or [p] or [ [p^2] ] (p = prime number).

The index for any of the infinite number of maximal isomorphic subgroups must be either a prime number p, or, in certain cases of tetragonal, trigonal and hexagonal space groups, a square of a prime number [p^2] ; for isomorphic subgroups of cubic space groups the index may only be the cube of a prime number [p^3] . In many instances only certain prime numbers are allowed (Bertaut & Billiet, 1979; Billiet & Bertaut, 2005; Müller & Brelle, 1995). If restrictions exist, the prime numbers allowed are given under the axes transformations by formulae such as ` $[p = {\rm prime} = 3n-1]$ '.

References

Bertaut, E. F. & Billiet, Y. (1979). On equivalent subgroups and supergroups of the space groups. Acta Cryst. A35, 733–745.Google Scholar

Billiet, Y. & Bertaut, E. F. (2005). Isomorphic subgroups of space groups. International Tables for Crystallography, Vol. A, Space-group symmetry, edited by Th. Hahn, Part 13. Heidelberg: Springer.Google Scholar

Müller, U. & Brelle, A. (1995). Über isomorphe Untergruppen von Raumgruppen der Kristallklassen , $[{\bar 4}]$ , , , $[{\bar 3}]$ , , $[{\bar 6}]$ und . Acta Cryst. A51, 300–304.Google Scholar

International Tables for Crystallography (2006). Vol. A1. ch. 3.1, p. 429