How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax
  Remote Access

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)
Published electronically: June 16, 2015
Keywords:Finite groups, finite simple groups, Sylow subgroups

View full volume PDF

View other years and numbers:

Table of Contents


  • 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 $4$


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.

References [Enhancements On Off] (What's this?)