03345nam 22006975 450 991076028030332120240626162315.03-031-39489-59783031394898(ebook)10.1007/978-3-031-39489-8(MiAaPQ)EBC30847526(Au-PeEL)EBL30847526(DE-He213)978-3-031-39489-8(CKB)28645349500041(EXLCZ)992864534950004120231101h20232023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierHypergroups /Paul-Hermann ZieschangCham :Springer,[2023]©20231 online resource (398 pages)Print version: Zieschang, Paul-Hermann Hypergroups Cham : Springer International Publishing AG,c2023 9783031394881 Includes bibliographical references and index.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.HypergroupsGroup theoryDiscrete mathematicsGraph theoryGeometryGroup Theory and GeneralizationsDiscrete MathematicsGraph TheoryGeometryTeoria de grafsthubGeometriathubLlibres electrònicsthubHypergroups.Group theory.Discrete mathematics.Graph theory.Geometry.Group Theory and Generalizations.Discrete Mathematics.Graph Theory.Geometry.Teoria de grafsGeometria512.2Zieschang Paul-Hermann1953-61061MiAaPQMiAaPQMiAaPQBOOK9910760280303321Hypergroups3598747UNINA