CI-groups with respect to ternary relational structures: new examples

Abstract

We find a sufficient condition to establish that certain abelian groups are not CI-groups with respect to ternary relational structures, and then show that the groups ${\mathbb{Z}}_3\times {\mathbb{Z}}_2^2$, ${\mathbb{Z}}_7\times {\mathbb{Z}}_2^3$, and ${\mathbb{Z}}_5\times {\mathbb{Z}}_2^4$ satisfy this condition. Then we completely determine which groups ${\mathbb{Z}}_2^3\times {\mathbb{Z}}_p$, $p$ a prime, are CI-groups with respect to binary and ternary relational structures. Finally, we show that ${\mathbb{Z}}_2^5$ is not a CI-group with respect to ternary relational structures.