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Overgroups of Sylow subgroups in sporadic groups
About this Title
Michael Aschbacher
Publication: Memoirs of the American Mathematical Society
Publication Year:
1986; Volume 60, Number 343
ISBNs: 978-0-8218-2344-6 (print); 978-1-4704-0759-9 (online)
DOI: https://doi.org/10.1090/memo/0343
MathSciNet review: 831891
MSC: Primary 20D08; Secondary 20B25, 20D05
Table of Contents
Chapters
- 1. Introduction
- 2. Preliminary lemmas
- 3. A generation lemma
- 4. A lemma on the representations of $\textrm {SL}_2(q)$
- 5. Certain subgroups of symplectic groups
- 6. Groups generated by transvections
- 7. Some subgroups of alternating groups
- 8. Large p-subgroups of finite groups
- 9. Centralizers of semisimple elements in groups of Lie type
- 10. Centralizers of unipotent elements in groups of Lie type
- 11. 3-structure in Sz and Ly
- 12. 2-structure in certain sporadic groups
- 13. 3-structure in $J_3$
- 14. 3-structure in $F_3$
- 15. Some subgroups of the Monster
- 16. Some groups with abelian Sylow groups
- 17. Groups of $\textrm {GF}(p)$-type
- 18. Almost simple groups of $\textrm {GF}(p)$-type
- 19. Random lemmas on groups of $\textrm {GF}(p)$-type
- 20. The proof of Theorem B
- 21. Large extraspecial subgroups of width 1
- 22. Large extraspecial 5-subgroups of width 1
- 23. Nonlocal overgroups of large symplectic subgroups
- 24. Small Sylow 3-groups
- 25. Overgroups of elementary abelian $p$-groups
- 26. Small overgroups of large symplectic $p$-subgroups
- 27. Geometries
- 28. Parabolics
- 29. Overgroups of Sylow $p$-groups in groups of $\textrm {GF}(p)$-type
- 30. Overgroups of large symplectic 2-subgroups
- 31. The Todd module
- 32. Geometries for $^2E_6(2)$ and $M(22)$
- 33. A 112-dimensional module $\textrm {GF}(2)J_4$-module