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 Z₃ × Z₂², Z₇ × Z₂³, and Z₅ × Z₂⁴ satisfy this condition. Then we completely determine which groups Z₂³ × Z_p, p a prime, are CI-groups with respect to color binary and ternary relational structures. Finally, we show that Z₂⁵ is not a CI-group with respect to ternary relational structures.