International Tables for Crystallography

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International Tables for Crystallography (2006). Vol. A1, Section 1.2.4.3
General introduction to the subgroups of space groups
Hans Wondratschek. International Tables for Crystallography (2011). Vol. A1, ch. 1.2, pp. 7-24  [ doi:10.1107/97809553602060000791 ]

Abstract

This general introduction deals with the theory of the main subjects of this volume: space groups and their subgroups. After some general remarks, the definitions and the corresponding lemmata of mappings (and their description by matrices) and groups (in particular symmetry groups, their classifications and their subgroups) are given. The different types of subgroups are defined and explained using several examples. The practical use of the abstract group–subgroup relations of space groups is explained and demonstrated using examples of their application to domain structures in Section 1.2.7. The chapter closes with a list of the most important lemmata on group–subgroup relations between space groups (without proofs).


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.