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SUPERGROUPS – a computer program for the determination of the supergroups of the space groups
Author(s) -
Ivantchev S.,
Kroumova E.,
Aroyo M. I.,
PerezMato J. M.,
Igartua J. M.,
Madariaga G.,
Wondratschek H.
Publication year - 2002
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s002188980200732x
Subject(s) - group (periodic table) , space (punctuation) , supergroup , space group , homogeneous space , mathematics , combinatorics , chemistry , computer science , physics , geometry , x ray crystallography , organic chemistry , geology , geochemistry , diffraction , optics , operating system
The problem of the determination of the supergroups of a given space group is of rather general interest. It is useful in phase-transition problems, in the search for overlooked symmetries in a crystal structure determination, or in the detection of pseudosymmetries as a tool for predicting higher-temperature phase transitions (Igartua et al., 1996). In all these applications, it is not suf®cient to know the space-group types of the supergroups of a given group; rather, it is necessary to have available all the different supergroups Gj > H which are isomorphic to G, and are of the same index [i]. In the literature, there are very few papers treating the supergroups of space groups in any detail (Koch, 1984; Wondratschek & Aroyo, 2001). In the International Tables for Crystallography, Vol. A, Space Group Symmetry (1983), one ®nds only listings of minimal supergroups of space groups, which, in addition, are not explicit: they only provide for each space group H the list of those space-group types in which H occurs as a maximal subgroup, i.e to which minimal supergroups of H belong. It is rather dif®cult to determine all supergroups Gj > H if only the types of the minimal supergroups are known. The program SUPERGROUPS solves this problem for a given ®nite index [i].