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Hypergroups / by Paul-Hermann Zieschang
版 | 1st ed. 2023. |
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出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2023 |
本文言語 | 英語 |
大きさ | XV, 391 p : online resource |
著者標目 | *Zieschang, Paul-Hermann author SpringerLink (Online service) |
件 名 | LCSH:Group theory LCSH:Discrete mathematics LCSH:Graph theory LCSH:Geometry FREE:Group Theory and Generalizations FREE:Discrete Mathematics FREE:Graph Theory FREE:Geometry |
一般注記 | 1 Basic Facts -- 2 Closed Subsets -- 3 Elementary Structure Theory -- 4 Subnormality and Thin Residues -- 5 Tight Hypergroups -- 6 Involutions -- 7 Hypergroups with a Small Number of Elements -- 8 Constrained Sets of Involutions -- 9 Coxeter Sets of Involutions -- 10 Regular Actions of (Twin) Coxeter Hypergroups This book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are developed along the lines of the structure theory of groups. The focus then turns to a number of concrete classes of hypergroups with small parameters, and continues with a closer look at the role of involutions (modeled after the definition of group-theoretic involutions) within the theory of hypergroups. Hypergroups generated by involutions lead to the exchange condition (a genuine generalization of the group-theoretic exchange condition), and this condition defines the so-called Coxeter hypergroups. Coxeter hypergroups can be treated in a similar way to Coxeter groups. On the other hand, their regular actions are mathematically equivalent to buildings (in the sense of Jacques Tits). A similar equivalence is discussed for twin buildings. The primary audience for the monograph will be researchers working in Algebra and/or Algebraic Combinatorics, in particular on association schemes HTTP:URL=https://doi.org/10.1007/978-3-031-39489-8 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783031394898 |
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電子リソース |
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EB00224341 |