Classification of regular Cayley maps of skew-type three on semidihedral groups

Kan Hu; Tao Qiu

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arXiv · 2606.26570

Classification of regular Cayley maps of skew-type three on semidihedral groups

Kan Hu·Tao Qiu

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Abstract

It is well known that every regular Cayley map $M = \CM(G,X,p)$ on a finite group $G$ with respect to an inverse-closed generating set $X$ of $G$ and a specified cyclic permutation $p$ on $X$ corresponds to a skew morphism $\varphi$ on $G$ such that the restriction of $\varphi$ to $X$ is $p$. The skew-type of the map $M$ is defined as the index $[G:\Ker \varphi]$, which equals the number of distinct values in $\mathbb{Z}_{|\varphi|}$ taken by the associated power function $\pi$ of the skew morphism $\varphi$. In this paper, we develop a covering theory of skew morphisms and as an application we provide a classification of regular Cayley maps of skew-type three on the semidihedral groups.

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Kan Hu, Tao Qiu. 2026-06-25. Classification of regular Cayley maps of skew-type three on semidihedral groups. https://arxiv.org/abs/2606.26570

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