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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

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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