The finite simple groups come in several infinite families (alternating groups and the group of Lie type) plus 26 sporadic groups. A leisurely and rigorous study of two of three generations of sporadic groups is the purpose of the book. The level is suitable for graduate students with little background in general finite group theory, established mathematicians and mathematical physicists.

Inhalt

1. Background from General Group Theory.- 2. Assumed Results about Particular Groups.- 3. Codes.- 4. The Hexacode.- 5. The Golay Code.- 6. Subgroups of M24.- 7. The Ternary Golay Code and 2·M12.- 8. Lattices.- 9. The Leech Lattice and Conway Groups.- 10. Subgroups of the Conway Groups; the Simple Groups of Higman-Sims, McLaughlin, Hall-Janko and Suzuki; Local Subgroups; Conjugacy Classes.- 11. Generation Three of the Happy Family and the Pariahs.- Appendix. Some Comments on the Atlas.- References.- List of Group Theoretic Notations.- The Orders of the Finite Simple Groups.