#### How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

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
Email: cust-serv@ams.org

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

# memo_has_moved_text();Reduced fusion systems over $2$-groups of sectional rank at most $4$

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

View full volume PDF

View other years and numbers:

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 $2$-groups of sectional rank at most $4$. The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional $2$-rank at most $4$. 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.