An Overview of the Foundations of the Hypergroup Theory

Christos Massouros and Gerasimos Massouros
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Christos Massouros: Core Department, Euripus Campus, National and Kapodistrian University of Athens, GR 34400 Euboia, Greece
Gerasimos Massouros: School of Social Sciences, Hellenic Open University, Aristotelous 18, GR 26335 Patra, Greece

Mathematics, 2021, vol. 9, issue 9, 1-41

Abstract: This paper is written in the framework of the Special Issue of Mathematics entitled “Hypercompositional Algebra and Applications”, and focuses on the presentation of the essential principles of the hypergroup, which is the prominent structure of hypercompositional algebra. In the beginning, it reveals the structural relation between two fundamental entities of abstract algebra, the group and the hypergroup. Next, it presents the several types of hypergroups, which derive from the enrichment of the hypergroup with additional axioms besides the ones it was initially equipped with, along with their fundamental properties. Furthermore, it analyzes and studies the various subhypergroups that can be defined in hypergroups in combination with their ability to decompose the hypergroups into cosets. The exploration of this far-reaching concept highlights the particularity of the hypergroup theory versus the abstract group theory, and demonstrates the different techniques and special tools that must be developed in order to achieve results on hypercompositional algebra.

Keywords: group; hypergroup; subhypergroup; cosets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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