幂零性：分解定理与阿贝尔性分类
Nilpotent dessins: Decomposition theorem and classification of the abelian dessins
摘要：
映射是可定向闭曲面的2-胞腔剖分。一个图是一个顶点着色固定的二分图。一个dessin是正则的，如果它的一组颜色和方向保持自同构的作用传递的边缘，和一个正则dessin是对称的，如果它允许一个额外的外部对称转置顶点颜色。研究了具有幂零自同构群正则设计。我们证明了每一个这样的Dessin是一个平行积的正则Dessins的自同构群的Sylow子群。对具有交换自同构群的正则和对称系统进行了分类和列举。
英文摘要：
A map is a 2-cell decomposition of an orientable closed surface. A dessin is a bipartite map with a fixed colouring of vertices. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the edges, and a regular dessin is symmetric if it admits an additional external symmetry transposing the vertex colours. Regular dessins with nilpotent automorphism groups are investigated. We show that each such dessin is a parallel product of regular dessins whose automorphism groups are the Sylow subgroups. Regular and symmetric dessins with abelian automorphism groups are classified and enumerated.
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