Woodslane | Book - 9781470456658

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Quaternion Fusion Packets

ISBN-13: 9781470456658
Publisher: AMERICAN MATHEMATICAL SOCIETY
Imprint: AMERICAN MATHEMATICAL SOCIETY
By Michael Aschbacher
Price: AUD $319.00
Stock: 0 in stock
Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
Local release date: 28/08/2021
Format: Paperback (254.00mm X 178.00mm) 456 pages Weight: 794g
Categories: Groups & group theory [PBG]

Description
Author Biography
Table of Contents
Google Preview: 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.; Michael Aschbacher, California Institute of Technology, Pasadena, CA; 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.; Google Preview content

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