International Tables for Crystallography (2016). Vol. A. ch. 1.1, pp. 2-11https://doi.org/10.1107/97809553602060000919

# Chapter 1.1. A general introduction to groups

## Contents

• 1.1. A general introduction to groups  (pp. 2-11)
• 1.1.1. Introduction  (p. 2) | html | pdf |
• 1.1.2. Basic properties of groups  (pp. 2-4) | html | pdf |
• 1.1.3. Subgroups  (pp. 4-5) | html | pdf |
• 1.1.4. Cosets  (pp. 5-6) | html | pdf |
• 1.1.5. Normal subgroups, factor groups  (pp. 6-7) | html | pdf |
• 1.1.6. Homomorphisms, isomorphisms  (pp. 7-9) | html | pdf |
• 1.1.7. Group actions  (pp. 9-10) | html | pdf |
• 1.1.8. Conjugation, normalizers  (pp. 10-11) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 1.1.2.1. Symmetry group 2mm of a rectangle  (p. 3) | html | pdf |
• Fig. 1.1.2.2. Symmetry group 3m of an equilateral triangle  (p. 3) | html | pdf |
• Fig. 1.1.2.3. Symmetry group 4mm of the square  (p. 3) | html | pdf |
• Fig. 1.1.3.1. Subgroup diagram for the symmetry group 3m of an equilateral triangle  (p. 4) | html | pdf |
• Fig. 1.1.3.2. Subgroup diagram for the symmetry group 2mm of a rectangle  (p. 5) | html | pdf |
• Fig. 1.1.3.3. Subgroup diagram for the symmetry group 4mm of the square  (p. 5) | html | pdf |
• Fig. 1.1.5.1. Symmetry group of an eightfold star  (p. 7) | html | pdf |
• Fig. 1.1.6.1. Schematic description of a homomorphism  (p. 8) | html | pdf |
• Fig. 1.1.6.2. Cyclic group of order 6 embedded in the group of the unit circle  (p. 8) | html | pdf |
• Fig. 1.1.7.1. Stabilizers in the symmetry group 4mm of the square  (p. 10) | html | pdf |