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Hypergroups by Paul-Hermann Zieschang

Hypergroups

by Paul-Hermann Zieschang
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Book cover type: Hardcover
  • ISBN13: 9783031394881
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 391
  • Original Price: EUR 139.99
  • Language: English
  • Edition: 2023
  • Item Weight: 744 grams
  • BISAC Subject(s): Algebra / Abstract, Combinatorics, and Graphic Methods

From the Back Cover

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.

Paul-Hermann Zieschang received his doctoral degree from the Christian-Albrechts-Universität zu Kiel (Germany), where he also completed his Habilitation. After holding temporary positions at Kansas State University and Kyushu University (Fukuoka), he joined the Department of Mathematics of the University of Texas at Brownsville. Since 2015, he has been Full Professor at the University of Texas Rio Grande Valley. The focus of his mathematical research is on finite groups, association schemes, and hypergroups.

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