Book contents
- Frontmatter
- Dedication
- Contents
- Figures
- Tables
- Preface
- Acknowledgements
- 1 Introduction
- 2 Steiner Systems
- 3 The Miracle Octad Generator
- 4 The Binary Golay Code
- 5 Uniqueness of the Steiner System S(5, 8, 24) and the Group M24
- 6 The Hexacode
- 7 Elements of the Mathieu Group M24
- 8 The Maximal Subgroups of M24
- 9 The Mathieu Group M24
- 10 The Leech Lattice M24
- 11 The Conway Group ·O
- 12 Permutation Actions of M24
- 13 Natural Generators of the Mathieu Groups
- 14 Symmetric Generation Using M24
- 15 The Thompson Chain of Subgroups of Co1
- Appendix MAGMA Code for 7★36 : A9 ↦ Co1
- References
- Index
1 - Introduction
Published online by Cambridge University Press: 31 October 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Figures
- Tables
- Preface
- Acknowledgements
- 1 Introduction
- 2 Steiner Systems
- 3 The Miracle Octad Generator
- 4 The Binary Golay Code
- 5 Uniqueness of the Steiner System S(5, 8, 24) and the Group M24
- 6 The Hexacode
- 7 Elements of the Mathieu Group M24
- 8 The Maximal Subgroups of M24
- 9 The Mathieu Group M24
- 10 The Leech Lattice M24
- 11 The Conway Group ·O
- 12 Permutation Actions of M24
- 13 Natural Generators of the Mathieu Groups
- 14 Symmetric Generation Using M24
- 15 The Thompson Chain of Subgroups of Co1
- Appendix MAGMA Code for 7★36 : A9 ↦ Co1
- References
- Index
Summary
We emphasize the unique position enjoyed by the Mathieu groups as the only quadruply or quintuply transitive permutation groups that exist, other than the alternating and symmetric groups. Their involvement in the largest Conway group ·O, the Monster group M and many other exceptional sporadic simple groups is mentioned. Brief descriptions of several of the most important constructions of the group M24 are given.
- Type
- Chapter
- Information
- The Art of Working with the Mathieu Group M24 , pp. 1 - 5Publisher: Cambridge University PressPrint publication year: 2024