Skew Product Groups for 2-Groups of Maximal Class

Skew morphisms, which generalise automorphisms for groups, provide a fundamental tool for the study of regular Cayley maps and, more generally, for finite groups with a complementary factorisation $X = GY$, where $Y$ is cyclic and core-free in $X$. $X$ is called the skew product group associated with $G$ and $Y$. In this paper, we classify skew product groups for the maximal class 2-groups.