CI-groups for ternary structures

TL;DR

This paper classifies all CI-groups for certain ternary relational structures, specifically those formed by cyclic groups combined with dicyclic or dihedral groups, extending known results to more complex structures.

Contribution

It explicitly determines all CI-groups of the form C × D with specified D groups, broadening the understanding of CI-group classifications for ternary structures.

Findings

All such groups are CI-groups for ternary structures.

These groups are also CI-groups for graphs and digraphs.

Provides a complete classification for the specified group products.

Abstract

We explicitly determine all CI-groups with respect to ternary relational structures that have the form $C \times D$, where $C$ is cyclic and $D$ is either a dicyclic group whose order is not divisible by $3$ or a dihedral group. Such groups are also CI-groups with respect to graphs and digraphs.