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Quaternion Fusion Packets.
・ISBN 978-1-4704-5665-8 paper US$ 122.00
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| 著者・編者 | Aschbacher, Michael, |
|---|---|
| シリーズ | Contemporary Mathematics |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2021 |
| ページ数 | 456 pp. |
| 言語 | ENG |
| ニュース番号 | <M25-12553> |
解説
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.