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Classification of regular maps of prime characteristic revisited: Avoiding the Gorenstein-Walter theorem
Journal of Algebra ( IF 0.8 ) Pub Date : 2020-04-01 , DOI: 10.1016/j.jalgebra.2019.12.008
Marston Conder , Jozef Širáň

Abstract Breda, Nedela and Siraň (2005) classified the regular maps on surfaces of Euler characteristic −p for every prime p. This classification relies on three key theorems, each proved using the highly non-trivial characterisation of finite groups with dihedral Sylow 2-subgroups, due to D. Gorenstein and J.H. Walter (1965). Here we give new proofs of those three facts (and hence the entire classification) using somewhat more elementary group theory, using without referring to the Gorenstein-Walter theorem.

中文翻译:

重访素数特征正则图的分类:避免 Gorenstein-Walter 定理

摘要 Breda、Nedela 和 Siraň (2005) 对每个素数 p 的欧拉特征 -p 表面上的正则映射进行分类。这种分类依赖于三个关键定理,每个定理都使用具有二面体 Sylow 2 子群的有限群的高度非平凡表征来证明,这要归功于 D. Gorenstein 和 JH Walter (1965)。在这里,我们使用更基本的群论,而不使用 Gorenstein-Walter 定理,对这三个事实(以及整个分类)给出了新的证明。
更新日期:2020-04-01
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