Smooth skew morphisms of the dihedral groups - Wang, Naer (Ars mathematica contemporanea, 2019)
A skew morphism ?$φ$? of a finite group ?$A$? is a permutation on ?$A$? fixing the identity element of ?$A$? and for which there exists an integer-valued function ?$π$? on ?$A$? such that ?$φ(ab) = φ(a)φ^{π(a)}(b)$? for all ?$a, b \in A$?. In the case where ?$π(φ(a)) = π(a)$?, for all ?$a \in A$?, the skew morphism is smooth. The concept of smooth skew morphism is a generalization of that of ?$t$?-balanced skew morphism. The aim of this paper is to develop a general theory of smooth skew morphisms. As an application we classify smooth skew morphisms of dihedral groups.
Keywords: Cayley map; Cayleyjev zemljevid; connected dominating set; gladka podgrupa; poševni morfizem; skew morphism; smooth subgroup