LEADER 03345nam 22006975 450 001 9910760280303321 005 20240626162315.0 010 $a3-031-39489-5 010 $a9783031394898$b(ebook) 024 7 $a10.1007/978-3-031-39489-8 035 $a(MiAaPQ)EBC30847526 035 $a(Au-PeEL)EBL30847526 035 $a(DE-He213)978-3-031-39489-8 035 $a(CKB)28645349500041 035 $a(EXLCZ)9928645349500041 100 $a20231101h20232023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHypergroups /$fPaul-Hermann Zieschang 210 1$aCham :$cSpringer,$d[2023] 210 4$d©2023 215 $a1 online resource (398 pages) 311 08$aPrint version: Zieschang, Paul-Hermann Hypergroups Cham : Springer International Publishing AG,c2023 9783031394881 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aThis 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. 606 $aHypergroups 606 $aGroup theory 606 $aDiscrete mathematics 606 $aGraph theory 606 $aGeometry 606 $aGroup Theory and Generalizations 606 $aDiscrete Mathematics 606 $aGraph Theory 606 $aGeometry 606 $aTeoria de grafs$2thub 606 $aGeometria$2thub 608 $aLlibres electrònics$2thub 615 0$aHypergroups. 615 0$aGroup theory. 615 0$aDiscrete mathematics. 615 0$aGraph theory. 615 0$aGeometry. 615 14$aGroup Theory and Generalizations. 615 24$aDiscrete Mathematics. 615 24$aGraph Theory. 615 24$aGeometry. 615 $aTeoria de grafs 615 7$aGeometria 676 $a512.2 700 $aZieschang$b Paul-Hermann$f1953-$061061 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910760280303321 996 $aHypergroups$93598747 997 $aUNINA