On multivalued groups of order 3

TL;DR

This paper provides a comprehensive classification of multivalued coset groups of order 3, utilizing the classification of rank 3 groups with regular normal subgroups to establish the results.

Contribution

It offers the first complete classification of multivalued coset groups of order 3, expanding the understanding of their structure and properties.

Findings

Complete classification of multivalued coset groups of order 3

Identification of key structural properties of these groups

Connection to rank 3 groups with regular normal subgroups

Abstract

A complete classification of the multivalued coset groups of order $3$ is given. The proof is based on the classification of rank $3$ groups having regular normal subgroups.