Paul-Hermann Zieschang: Hypergroups | Buch

Cover: 9783031394881 | Hypergroups | Paul-Hermann Zieschang | Buch | xv | Englisch | 2023

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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 with a neutral element

The approach relates to different algebraic and geometric objects (groups, association schemes, buildings)

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2023
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xv 391 S.
ISBN-13:	9783031394881
ISBN-10:	3031394887
Sprache:	Englisch
Einband:	Gebunden
Autor:	Zieschang, Paul-Hermann
Auflage:	1st edition 2023
Hersteller:	Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 28 mm
Von/Mit:	Paul-Hermann Zieschang
Erscheinungsdatum:	02.11.2023
Gewicht:	0,776 kg

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