Smooth skew morphisms of the dihedral groups

Na-Er Wang, Kan Hu, Kai Yuan, Jun-Yang Zhang

Abstract


A skew morphism φ of a finite group A is a permutation on A fixing the identity element of A and for which there exists an integer-valued function π on A such that φ(ab) = φ(a)φπ(a)(b) for all a, b ∈ A. In the case where π(φ(a)) = π(a), for all a ∈ A, the skew morphism is smooth. The concept of smooth skew morphism is a generalization of that of t-balanced skew morphism. The aim of this paper is to develop a general theory of smooth skew morphisms. As an application we classify smooth skew morphisms of dihedral groups.


Keywords


Cayley map, skew morphism, smooth subgroup

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DOI: https://doi.org/10.26493/1855-3974.1475.3d3

ISSN: 1855-3974

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