The Degrees Of Toroidal Regular Proper Hypermaps
Maria Elisa Fernandes, Claudio Alexandre Piedade

TL;DR
This paper completes the classification of symmetry groups of regular toroidal hypermaps of type (3,3,3) on genus 1 surfaces, focusing on subgroups of index 2 of the symmetry group of a specific toroidal map.
Contribution
It provides a detailed analysis of the subgroup structure related to regular toroidal hypermaps of type (3,3,3) on genus 1 surfaces, extending previous classifications.
Findings
Classification of subgroups of index 2 in the symmetry group of a toroidal map.
Identification of hypermaps of type (3,3,3) on genus 1 surfaces.
Completion of the symmetry classification for these hypermaps.
Abstract
Recently the classification of all possible faithful transitive permutation representations of the group of symmetries of a regular toroidal map was accomplished. In this paper we complete this investigation on a surface of genus 1 considering the group of a regular toroidal hypermap of type that is a subgroup of index of the group of symmetries of a toroidal map of type .
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