On elementary abelian 2-hypergroups

TL;DR

This paper investigates the structure of elementary abelian 2-hypergroups, classifying their closed subsets, normal subsets, automorphisms, and isomorphisms to deepen understanding of their algebraic properties.

Contribution

It provides a complete classification of closed and strongly normal closed subsets, automorphism groups, and isomorphism criteria for elementary abelian 2-hypergroups.

Findings

All closed subsets are classified.

Automorphism groups of closed subsets are determined.

Criteria for isomorphism of closed subsets are established.

Abstract

A hypergroup is called an elementary abelian 2-hypergroup if it is a constrained direct product of the closed subsets of two elements. In this paper, the elementary abelian 2-hypergroups are studied. All closed subsets and all strongly normal closed subsets of the elementary abelian 2-hypergroups are determined. The numbers of all closed subsets and all strongly normal closed subsets of the elementary abelian 2-hypergroups are given. A criterion for the isomorphic closed subsets of the elementary abelian 2-hypergroups is displayed. The automorphism groups of all closed subsets of the elementary abelian 2-hypergroups are presented.