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Lemmata on maximal subgroups
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.2.8.2, pp. 23-24 [ doi:10.1107/97809553602060000791 ]
Lemmata on maximal subgroups 1.2.8.2. Lemmata on maximal subgroups Even the set of all maximal subgroups of finite index is not finite, as can be seen from the following lemma. Lemma 1.2.8.2.1.The index i of a maximal subgroup of a space group is always of the form , where p is a ...
     [more results from section 1.2.8 in volume A1]

Examples
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.2.7.3, pp. 22-23 [ doi:10.1107/97809553602060000791 ]
Examples 1.2.7.3. Examples The terms just defined shall be explained in a few examples. In Example 1.2.7.3.1 a translationengleiche transition is considered; i.e. is a translationengleiche subgroup of . Because , the relation between and is reflected by the relation between the space groups and and the results of the microscopic and ...
     [more results from section 1.2.7 in volume A1]

The role of normalizers for group-subgroup pairs of space groups
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.2.6.3, pp. 19-20 [ doi:10.1107/97809553602060000791 ]
The role of normalizers for group-subgroup pairs of space groups 1.2.6.3. The role of normalizers for group-subgroup pairs of space groups In Section 1.2.4.5, the normalizer of a subgroup in the group was defined. The equation holds, i.e. is a normal subgroup of . The normalizer , by its index ...
     [more results from section 1.2.6 in volume A1]

Crystal systems and crystal families
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.2.5.5, pp. 17-18 [ doi:10.1107/97809553602060000791 ]
... crystal class C of a space group is either holohedral H or it can be assigned uniquely to H by the condition: any point group of C is a subgroup of a point group of H but not a subgroup of a holohedral crystal class ...
     [more results from section 1.2.5 in volume A1]

Normalizers
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.2.4.5, pp. 13-14 [ doi:10.1107/97809553602060000791 ]
Normalizers 1.2.4.5. Normalizers The concept of the normalizer of a group in a group is very useful for the considerations of the following sections. The length of the conjugacy class of in is determined by this normalizer. Let and . Then holds because is a group. If , then for any . ...
     [more results from section 1.2.4 in volume A1]

Group isomorphism and homomorphism
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.2.3.2, pp. 11-12 [ doi:10.1107/97809553602060000791 ]
Group isomorphism and homomorphism 1.2.3.2. Group isomorphism and homomorphism A finite group of small order may be conveniently visualized by its multiplication table, group table or Cayley table. An example is shown in Table 1.2.3.1. Table 1.2.3.1| | Multiplication table of a group The group elements are listed at the top of ...
     [more results from section 1.2.3 in volume A1]

Origin shift and change of the basis
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.2.2.7, p. 10 [ doi:10.1107/97809553602060000791 ]
... in IT A Chapters 5.1 and 5.2 , and in Hahn & Wondratschek (1994). Let a coordinate system be given with a ... only remains because of the equality . References Hahn, Th. & Wondratschek, H. (1994). Symmetry of Crystals. Introduction to International Tables ...
     [more results from section 1.2.2 in volume A1]

General remarks
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.2.1, p. 7 [ doi:10.1107/97809553602060000791 ]
General remarks 1.2.1. General remarks The performance of simple vector and matrix calculations, as well as elementary operations with groups, are nowadays common practice in crystallography, especially since computers and suitable programs have become widely available. The authors of this volume therefore assume that the reader has at least some practical ...

General introduction to the subgroups of space groups
Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, ch. 1.2, pp. 7-24 [ doi:10.1107/97809553602060000791 ]
... be found in IT A, Part 11 or in Hahn & Wondratschek (1994). 1.2.2.6. Vectors and vector coefficients | | In crystallography, vectors ... in IT A Chapters 5.1 and 5.2 , and in Hahn & Wondratschek (1994). Let a coordinate system be given with a ... Introduction to International Tables for Crystallography, Vol. A by Hahn & Wondratschek (1994) describes a way in which the data of ...

Applications of group-subgroup relations
Aroyo, M. I., Müller, U. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.1.4, pp. 4-5 [ doi:10.1107/97809553602060000790 ]
... to V3Si. Chem. Phys. Lett. 1, 69-72. Bärnighausen, H. (1980). Group-subgroup relations between space groups: a useful ... chemistry. MATCH Commun. Math. Chem. 9, 139-175. Baur, W. H. & Kassner, D. (1992). The perils of Cc: comparing the ... Chim. Acta, 52, 2333-2347. Janovec, V., Hahn, Th. & Klapper, H. (2003). Twinning and domain structures. International Tables for ...

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