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Reduced fusion systems over $2$-groups of sectional rank at most $4$
About this Title
Bob Oliver, Université Paris 13, Sorbonne Paris Cité, LAGA, UMR 7539 du CNRS, 99, Av. J.-B. Clément, 93430 Villetaneuse, France
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: https://doi.org/10.1090/memo/1131
Published electronically: June 16, 2015
Keywords: Finite groups,
finite simple groups,
Sylow subgroups,
fusion
MSC: Primary 20D20; Secondary 20D05, 20E32, 20E45
Table of Contents
Chapters
- Introduction
- 1. Background on fusion systems
- 2. Normal dihedral and quaternion subgroups
- 3. Essential subgroups in $2$-groups of sectional rank at most $4$
- 4. Fusion systems over $2$-groups of type $G_2(q)$
- 5. Dihedral and semidihedral wreath products
- 6. Fusion systems over extensions of $UT_3(4)$
- A. Background results about groups
- B. Subgroups of $2$-groups of sectional rank $4$
- C. Some explicit $2$-groups of sectional rank $4$
- 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.- Kasper K. S. Andersen, Bob Oliver, and Joana Ventura, Reduced, tame and exotic fusion systems, Proc. Lond. Math. Soc. (3) 105 (2012), no. 1, 87–152. MR 2948790, DOI 10.1112/plms/pdr065
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