Skew-morphisms of nonabelian characteristically simple groups

2019/12/27 by Chen, Jiyong, Du, Shaofei, Li, Cai Heng · 1 citation
#05A05 #05C25 #20B25 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.12013

Abstract

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

Cited by

• Hall Skew-morphisms and Hall Cayley maps of finite groups

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• Skew-Morphisms of Elementary Abelian p-Groups
• Classification of cyclic groups underlying only smooth skew morphisms
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• Quotients of skew morphisms of cyclic groups
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