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 Z 3 × Z 2 2 , Z 7 × Z 2 3 , and Z 5 × Z 2 4 satisfy this condition. Then we completely determine which groups Z 2 3 × Z p , p a prime, are CI-groups with respect to color binary and ternary relational structures. Finally, we show that Z 2 5 is not a CI-group with respect to ternary relational structures.
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