On the CI-property for balanced configurations

Sergio Hiroki Koike Quintanar University of Primorska

Dragan Marušič University of Primorska

Content: Let $G$ be a finite group. A Cayley object is a relational structure with underlying set $G$ which is invariant under all right translations $x \mapsto xg$, $x,g \in G$. Given a class $\mathcal{K}$ of Cayley objects of $G$, the group $G$ is said to satisfy the CI-property for $\mathcal{K}$ if for any two isomorphic Cayley objects in $\mathcal{K}$, there is an isomorphism between them, which is at the same time an automorphism of the group $G$. The question whether a given group $G$ satisfies the CI-property for a given class $\mathcal{K}$ of Cayley objects has been studied under various choices of $G$ and $\mathcal{K}$. In this talk, we focus our attention to the class of balanced configurations where we show that every cyclic group satisfy the CI-property.