Finite Simple Groups.
This volume contains the proceedings of the international conference Finite Simple Groups: Thirty Years of the Atlas and Beyond Celebrating the Atlases and Honoring John Conway, which was held from November 2-5, 2015, at Princeton University, Princeton, New Jersey. Classification of Finite Simple Gr...
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| Format: | eBook |
| Language: | English |
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American Mathematical Society,
2017.
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| Series: | Contemporary Mathematics.
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Table of Contents:
- Cover; Title page; Contents; Preface; Acknowledgments; Moonshine and the meaning of life; References; The Monster is fabulous; 1. Introduction; 2. Transposition Groups; 3.-diagrams; 4. Working in the Projective Plane; 5. Fabulous Groups; References; Majorana representation of the Monster group; 1. Majorana algebras; 2. The Monster algebra and Norton-Sakuma subalgebras; 3. Classifying Majorana representations; References; Letter to Donna Testerman; Reliability and reproducibility of Atlas information; 1. Introduction; 2. Maximal subgroups; 3. Character tables; Acknowledgments; References.
- 2. A more general setting for groupoids3. Conway groupoids and codes; 4. Classification results; 5. Generation games; References; The subgroup structure of finite groups; 1. Reductions for permutation groups; 2. The finite simple groups; 3. The alternating and symmetric groups; 4. Groups of Lie type; 5. Exceptional groups of Lie type; 6. The Palfy-Pudlak Question; 7. Lower signalizer lattices.; 8. A question and a theorem; References; Some remarks on maximal subgroups of finite classical groups; 1. Introduction; 2. Maximality of members of \SSS(): An overview.
- 3. Irreducible representations of ₁₁Acknowledgement; References; Toward a classification of endotrivial modules; 1. Introduction; 2. Definitions and preliminaries; 3. A little history; 4. The kernel of restriction and Green correspondents; 5. The kernel of restriction to the Sylow subgroup; 6. Another viewpoint; 7. Simple endotrivial modules; 8. Acknowledgments; References; Some remarks on global/local conjectures; 1. On the ()-Conjecture; 2. () and ; 3. AWC and the Glauberman Correspondence; Acknowledgements; References; Minuscule weights and Chevalley groups; 1. Introduction.
- 2. Minuscule weight modules3. Weyl group action; 4. Chevalley groups via minuscule weights; 5. Remarks and examples; References; A method for building permutation representations of finitely presented groups; 1. Introduction; 2. The construction of mosaics; 3. Some examples; References; Character ratios for finite groups of Lie type, and applications; 1. Introduction; 2. Previous results; 3. A new result; 4. Applications of Theorem 3.1; 5. Remarks on the proof of Theorem 3.1; References; Conjugacy classes, growth and complexity; 1. Introduction; 2. Covering; 3. Growth; 4. Mixing.
- Characters and Brauer trees of the covering group of ² ₆(2)1. Introduction; 2. The character table of \boldmath3. ; 3. Determination of Brauer trees; References; Maximal subgroups of sporadic groups; 1. Introduction; 2. Methods; 3. Historical survey; 4. Results; References; Construction of the Thompson Chain of subgroups of the Conway group ⋅ and complete graphs on letters; 1. Introduction; 2. The Leech lattice Λ; 3. The Miracle Octad Generator or MOG; 4. Verification of the presentation; 5. Conclusion; References; Conway's groupoid and its relatives; 1. The first Conway groupoid ₁₃