| 書目名稱 | Hypergroups | | 編輯 | Paul-Hermann Zieschang | | 視頻video | http://file.papertrans.cn/431/430644/430644.mp4 | | 概述 | The text provides a direct path from elementary algebraic and combinatorial observations to research problems.The book is the first attempt to systematically develop a structure theory of hypergroups | | 圖書封面 |  | | 描述 | .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.. | | 出版日期 | Book 2023 | | 關鍵詞 | 20N20, 20A05, 05E30; 51E24, 51E05, 51E15, 51F15, 20E42, 20F55, 20P99, 05Exx; hypergroup; association sc | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-39489-8 | | isbn_softcover | 978-3-031-39491-1 | | isbn_ebook | 978-3-031-39489-8 | | copyright | Springer Nature Switzerland AG 2023 |
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