International Tables for Crystallography (2011). Vol. A1. ch. 1.4, pp. 27-40   | 1 | 2 | https://doi.org/10.1107/97809553602060000793

# Chapter 1.4. The mathematical background of the subgroup tables

## Contents

• 1.4. The mathematical background of the subgroup tables  (pp. 27-40)
• 1.4.1. Introduction  (p. 27) | html | pdf |
• 1.4.2. The affine space  (pp. 27-29) | html | pdf |
• 1.4.2.1. Motivation  (p. 27) | html | pdf |
• 1.4.2.2. Vector spaces  (pp. 27-28) | html | pdf |
• 1.4.2.3. The affine space  (p. 28) | html | pdf |
• 1.4.2.4. The affine group  (pp. 28-29) | html | pdf |
• 1.4.3. Groups  (pp. 29-33) | html | pdf |
• 1.4.3.1. Groups  (pp. 29-30) | html | pdf |
• 1.4.3.2. Actions of groups on sets  (pp. 30-31) | html | pdf |
• 1.4.3.3. The Sylow theorems  (pp. 31-32) | html | pdf |
• 1.4.3.4. Isomorphisms  (p. 32) | html | pdf |
• 1.4.3.5. Isomorphism theorems  (pp. 32-33) | html | pdf |
• 1.4.3.6. An example  (p. 33) | html | pdf |
• 1.4.4. Space groups  (pp. 33-35) | html | pdf |
• 1.4.4.1. Definition of space groups  (pp. 33-34) | html | pdf |
• 1.4.4.2. Maximal subgroups of space groups  (pp. 34-35) | html | pdf |
• 1.4.5. Maximal subgroups  (pp. 35-37) | html | pdf |
• 1.4.5.1. Maximal subgroups and primitive -sets  (pp. 35-36) | html | pdf |
• 1.4.5.2. Soluble groups  (p. 36) | html | pdf |
• 1.4.5.3. Maximal subgroups of soluble groups  (pp. 36-37) | html | pdf |
• 1.4.6. Quantitative results  (pp. 37-38) | html | pdf |
• 1.4.6.1. General results  (p. 37) | html | pdf |
• 1.4.6.2. Three-dimensional space groups  (pp. 37-38) | html | pdf |
• 1.4.7. Qualitative results  (pp. 38-39) | html | pdf |
• 1.4.7.1. General theory  (p. 38) | html | pdf |
• 1.4.7.2. Three-dimensional space groups  (pp. 38-39) | html | pdf |
• 1.4.8. Minimal supergroups  (pp. 39-40) | html | pdf |
• References | html | pdf |