Polygroup Theory And Related Systems

This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics.
Contents:A Brief Excursion into Group Theory:IntroductionThe Abstract Definition of a Group and Some ExamplesSubgroupsNormal Subgroups and Quotient GroupsGroup HomomorphismsPermutation GroupsDirect ProductSolvable and Nilpotent GroupsHypergroups:Introduction and Historical Development of HypergroupsDefinitions and Examples of HypergroupsSome Kinds of SubhypergroupsHomomorphisms of HypergroupsRegular and Strongly Regular RelationsComplete HypergroupsJoin SpacesPolygroups:Definition and Examples of PolygroupsExtension of Polygroups by PolygroupsSubpolygroups and Quotient PolygroupsIsomorphism Theorems of Polygroupsγ* Relation on PolygroupsGeneralized PermutationsPermutation PolygroupsRepresentation of PolygroupsPolygroup HyperringsSolvable PolygroupsNilpotent PolygroupsWeak Polygroups:Weak HyperstructuresWeak Polygroups as a Generalization of PolygroupsFundamental Relations on Weak PolygroupsSmall Weak PolygroupsCombinatorial Aspects of Polygroups:Chromatic PolygroupsPolygroups Derived from CogroupsConjugation Lattice
Readership: Graduate students and researchers in algebraic hyperstructures and applications.