Totally symmetric dessins with nilpotent automorphism groups of class three

Na-Er Wang; Roman Nedela; Kan Hu

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arXiv · 1511.06863

Totally symmetric dessins with nilpotent automorphism groups of class three

Na-Er Wang·Roman Nedela·Kan Hu

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Abstract

A dessin is a 2-cell embedding of a connected bipartite graph into an orientable closed surface. An automorphism of a dessin is a permutation of the edges of the underlying graph which preserves the colouring of the vertices and extends to an orientation-preserving self-homeomorphism of the supporting surface. A dessin is regular if its automorphism group is transitive on the edges, and a regular dessin is totally symmetric if it is invariant under all dessin operations. Thus totally symmetric dessins possesses the highest level of external symmetry. In this paper we present a classification of totally symmetric dessins with a nilpotent automorphism group of class three

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BibTeX RIS

Na-Er Wang, Roman Nedela, Kan Hu. 2015-11-21. Totally symmetric dessins with nilpotent automorphism groups of class three. https://arxiv.org/abs/1511.06863

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