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Reduced fusion systems over $2$-groups of sectional rank at most $4$


About this Title

Bob Oliver

Publication: Memoirs of the American Mathematical Society
Publication Year: 2016; Volume 239, Number 1131
ISBNs: 978-1-4704-1548-8 (print); 978-1-4704-2745-0 (online)
DOI: http://dx.doi.org/10.1090/memo/1131
Published electronically: June 16, 2015
Keywords:Finite groups, finite simple groups, Sylow subgroups

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Table of Contents


Chapters

  • Introduction
  • Chapter 1. Background on fusion systems
  • Chapter 2. Normal dihedral and quaternion subgroups
  • Chapter 3. Essential subgroups in $2$-groups of sectional rank at most $4$
  • Chapter 4. Fusion systems over $2$-groups of type $G_2(q)$
  • Chapter 5. Dihedral and semidihedral wreath products
  • Chapter 6. Fusion systems over extensions of $\mathit {UT}_3(4)$
  • Appendix A. Background results about groups
  • Appendix B. Subgroups of $2$-groups of sectional rank $4$
  • Appendix C. Some explicit $2$-groups of sectional rank $4$
  • Appendix D. Actions on $2$-groups of sectional rank at most $4$

Abstract


We classify all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But our method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

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