Skew Product Groups for 2-Groups of Maximal Class

TL;DR

This paper classifies skew product groups associated with maximal class 2-groups, advancing understanding of their structure and role in the study of regular Cayley maps and group factorizations.

Contribution

It provides a complete classification of skew product groups for maximal class 2-groups, a key step in understanding their automorphisms and factorizations.

Findings

Classification of skew product groups for maximal class 2-groups

Insights into automorphisms and Cayley maps of these groups

Enhanced understanding of group factorizations involving cyclic subgroups

Abstract

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.