International Tables for Crystallography (2006). Vol. A1. ch. 1.5, pp. 29-40   | 1 | 2 | https://doi.org/10.1107/97809553602060000541

# Chapter 1.5. The mathematical background of the subgroup tables

## Contents

• 1.5. The mathematical background of the subgroup tables  (pp. 29-40)
• 1.5.1. Introduction  (p. 29) | html | pdf |
• 1.5.2. The affine space  (pp. 29-31) | html | pdf |
• 1.5.2.1. Motivation  (p. 29) | html | pdf |
• 1.5.2.2. Vector spaces  (pp. 29-30) | html | pdf |
• 1.5.2.3. The affine space  (p. 30) | html | pdf |
• 1.5.2.4. The affine group  (pp. 30-31) | html | pdf |
• 1.5.3. Groups  (pp. 31-34) | html | pdf |
• 1.5.3.1. Groups  (p. 31) | html | pdf |
• 1.5.3.2. Actions of groups on sets  (pp. 32-33) | html | pdf |
• 1.5.3.3. The Sylow theorems  (p. 33) | html | pdf |
• 1.5.3.4. Isomorphisms  (pp. 33-34) | html | pdf |
• 1.5.3.5. Isomorphism theorems  (p. 34) | html | pdf |
• 1.5.3.6. An example  (p. 34) | html | pdf |
• 1.5.4. Space groups  (pp. 34-36) | html | pdf |
• 1.5.4.1. Definition of space groups  (pp. 34-35) | html | pdf |
• 1.5.4.2. Maximal subgroups of space groups  (pp. 35-36) | html | pdf |
• 1.5.5. Maximal subgroups  (pp. 36-38) | html | pdf |
• 1.5.5.1. Maximal subgroups and primitive -sets  (pp. 36-37) | html | pdf |
• 1.5.5.2. Soluble groups  (p. 37) | html | pdf |
• 1.5.5.3. Maximal subgroups of soluble groups  (p. 38) | html | pdf |
• 1.5.6. Quantitative results  (pp. 38-39) | html | pdf |
• 1.5.6.1. General results  (p. 38) | html | pdf |
• 1.5.6.2. Three-dimensional space groups  (pp. 38-39) | html | pdf |
• 1.5.7. Qualitative results  (pp. 39-40) | html | pdf |
• 1.5.7.1. General theory  (p. 39) | html | pdf |
• 1.5.7.2. Three-dimensional space groups  (pp. 39-40) | html | pdf |
• References | html | pdf |