Classification of coset-preserving skew-morphisms of finite cyclic groups

The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-balanced skew-morphisms of regular Cayley maps which are in turn generalizations of group automorphisms. In case of abelian groups, all skew-morphisms of regular Cayley maps are roots of coset-preserving skew-morphisms, and therefore, classification of cosetpreserving skew-morphisms of finite abelian groups is the first step toward classification of all skew-morphisms of these groups. We present a characterization of coset-preserving skew-morphisms of finite cyclic groups, and devise an algorithm for their classification.