Quaternion fusion packets
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Bibliographic Information
Quaternion fusion packets
（Contemporary mathematics, 765）
American Mathematical Society, 2021
- : pbk
Available at / 21 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkS||CONM||765200041759935
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Note
Includes bibliographical references (p. 441-442) and index
Description and Table of Contents
Description
Let $p$ be a prime and$S$ a finite $p$-group. A $p$-fusion system on $S$ is a category whose objects are the subgroups of $S$ and whose morphisms are certain injective group homomorphisms. Fusion systems are of interest in modular representation theory, algebraic topology, and local finite group theory. The book provides a characterization of the 2-fusion systems of the groups of Lie type and odd characteristic, a result analogous to the Classical Involution Theorem for groups. The theorem is the most difficult step in a two-part program. The first part of the program aims to determine a large subclass of the class of simple 2-fusion systems, while part two seeks to use the result on fusion systems to simplify the proof of the theorem classifying the finite simple groups.
Table of Contents
Background and overview: Introduction
The major theorems and some background
Basics and examples:
Some basic results
Results on $\tau$
$W(\tau)$ and $M(\tau)$
Some examples
Theorems 2 through 5: Theorems 2 and 4
Theorems 3 and 5
Coconnectedness: $\tau^{\circ}$ not coconnected
Theorem 6: $\Omega =\Omega(z)$ of order 2
$\vert\Omega(z)\vert>2$
Some results on generation
$\vert\Omega(z)\vert=2$ and the proof of Theorem 6
Theorems 7 and 8: $\vert\Omega(z)\vert=1$ and $\mu$ abelian
More generation
$\vert\Omega(z)\vert=1$ and $\mu$ nonabelian
Theorem 1 and the Main Theorem: Proofs of four theorems
References and Index: Bibliography
Index.
by "Nielsen BookData"
