The Art of Working with the Mathieu Group M24

Autorentext
Robert T. Curtis is Emeritus Professor of Combinatorial Algebra at the University of Birmingham. He is the author of 'Symmetric Generation of Groups' (2007) and co-author of 'An Atlas of Finite Groups' (1985). He was the London Mathematical Society Librarian from 2003 to 2007 and Treasurer from 2011 to 2020.

Klappentext

The group M24 leads to the Leech lattice, leading to the largest Conway group, and thence to the Monster group. Every mathematician has heard of these structures; balancing theory and computation, the book explains where they come from, in a manner accessible to advanced undergraduates, research students and senior researchers.

Inhalt

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 M12; 10. The Leech lattice ; 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.