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Hypergroups

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Hypergroups/ by Paul-Hermann Zieschang.
作者:	Zieschang, Paul-Hermann.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xv, 391 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Geometry. -
電子資源:	https://doi.org/10.1007/978-3-031-39489-8
ISBN:	9783031394898

Hypergroups
Zieschang, Paul-Hermann.

Hypergroups[electronic resource] /by Paul-Hermann Zieschang. - Cham :Springer International Publishing :2023. - xv, 391 p. :ill., digital ;24 cm.

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.

ISBN: 9783031394898

Standard No.: 10.1007/978-3-031-39489-8doiSubjects--Topical Terms:

579899
Geometry.

LC Class. No.: QA174.2 / .Z547 2023

Dewey Class. No.: 512.2

Hypergroups
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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 2 4 $a Geometry. $3 579899
650 2 4 $a Graph Theory. $3 786670
650 2 4 $a Discrete Mathematics. $3 796600
650 1 4 $a Group Theory and Generalizations. $3 672112
650 0 $a Hypergroups. $3 1237313
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773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-39489-8
950 $a Mathematics and Statistics (SpringerNature-11649)