Hypergroups

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.

“This well-written book focuses on the abstract algebraic notion of hypergroup. ... This book is a very interesting, readable and descriptive text in the algebraic theory of hyperstructures and can be a good reference for researchers working in algebra.” (Dariush Heidari, zbMATH 1552.20002, 2025) “The book is written clearly, with attention to detail in both definitions and proofs, and the editorial choices make this book reader-friendly.” (Jan Gałuszka, Mathematical Reviews, December, 2024)

• 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.