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,...
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| Главный автор: | |
|---|---|
| Соавтор: | |
| Формат: | Электронный ресурс eКнига |
| Язык: | английский |
| Опубликовано: |
Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| Редактирование: | 1st ed. 2023. |
| Предметы: | |
| Online-ссылка: | https://doi.org/10.1007/978-3-031-39489-8 |
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| 100 | 1 | |a Zieschang, Paul-Hermann. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Hypergroups |h [electronic resource] / |c by Paul-Hermann Zieschang. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2023. | |
| 300 | |a XV, 391 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Discrete mathematics. | |
| 650 | 0 | |a Graph theory. | |
| 650 | 0 | |a Geometry. | |
| 650 | 1 | 4 | |a Group Theory and Generalizations. |
| 650 | 2 | 4 | |a Discrete Mathematics. |
| 650 | 2 | 4 | |a Graph Theory. |
| 650 | 2 | 4 | |a Geometry. |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031394881 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031394904 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031394911 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-39489-8 |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||