Skewmorphisms of nonabelian characteristically simple groups
Abstract
A skewmorphism of a finite group $G$ is a permutation $\s$ on $G$ fixing the identity element, and for which there exists an integer function $\pi$ on $G$ such that $\s(xy)=\s(x)\s^{\pi(x)}(y)$ for all $x,y\in G$. It has been known that given a skewmorphism $\s $ of $G$, the product of $\lg \s \rg$ with the left regular representation of $G$ forms a permutation group on $G$, called the skewproduct group of $\s$. The skewmorphism was introduced as an algebraic tool to investigate regular Cayley maps. In this paper, the skewproduct groups are characterized, for all skewmorphisms of finite nonabelian characteristically simple groups (see Theorem 1.1) and correspondingly the Cayley maps on these groups are characterized (see Theorem 1.5).
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.12013
 Bibcode:
 2019arXiv191212013C
 Keywords:

 Mathematics  Combinatorics;
 05C25;
 05A05;
 20B25
 EPrint:
 18 Pages