环群的完全正则解和反平衡斜态

Kan Hu, Young Soo Kwon
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引用次数: 1

摘要

有限群A的斜态射是A上的一个双射φ,固定A的单位元,并且在A上存在一个整值函数π,使得对于所有A, b∈A, φ(ab) = φ(A)φ(b)。此外,如果φ−1(A) = φ(A−1)−1,对于所有A∈A,则φ称为反平衡。本文建立了反平衡斜态射的一般理论,并建立了具有完全二部下图的挠性正则图的循环加性群和同构类的反平衡斜态射的倒易对之间的一一对应关系。作为一种应用,对柔性完全规则设计进行了分类。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Reflexible complete regular dessins and antibalanced skew morphisms of cyclic groups
A skew morphism of a finite group A is a bijection φ 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)φ(b), for all a, b ∈ A. In addition, if φ−1(a) = φ(a−1)−1, for all a ∈ A, then φ is called antibalanced. In this paper we develop a general theory of antibalanced skew morphisms and establish a one-to-one correspondence between reciprocal pairs of antibalanced skew morphisms of the cyclic additive groups and isomorphism classes of reflexible regular dessins with complete bipartite underlying graphs. As an application, reflexible complete regular dessins are classified.
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