Smooth skew-morphisms of the dihedral groups

Naer Wang, Kan Hu, Kai Yuan +1

A skew-morphism $\phi$ of a finite group $A$ is a permutation on $A$ such that $\phi (1)=1$ and $\phi (xy)=\phi (x){\phi }^{\pi (x)}(y)$ for all $x,y\in A$ where $\pi :A\to {\mathbb{Z}}_{|\phi |}$ is an integer fun…