A skew-morphism of a finite group G is a permutation σ on G fixing the identity element such that the product of $〈\sigma 〉$ with the left regular representation of G forms a permutation group on G. This permutation group is called the skew-product group of σ. The skew-morphism was introduced as an algebraic tool to investigate regular Cayley maps. In this paper, we characterize skew-products of skew-morphisms of finite nonabelian characteristically simple groups (see Theorem 1.2) and the corresponding regular Cayley maps (see Theorem 1.6).

中文翻译：

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非阿贝尔特征单群的偏态射

有限群的歪斜态射ģ是置换σ上ģ固定单位元，使得的产物$〈\sigma 〉$用的左正则表示ģ形成在置换群G ^。这个置换群称为σ的偏积群。偏态射被引入作为研究常规 Cayley 映射的代数工具。在本文中，我们刻画了有限非阿贝尔特征单群的偏态射的偏积（见定理 1.2）和相应的正则 Cayley 映射（见定理 1.6）。