紧致非定向黎曼曲面上的阿贝尔作用

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal Pub Date : 2021-12-02 DOI:10.1017/S0017089521000410

Jesús Rodríguez

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引用次数: 1

摘要

摘要给定整数$g>2$，给出了有限阿贝尔群作为g属的紧致不可定向Riemann曲面的自同构群的充要条件，为求阿贝尔群的对称交叉帽数提供了一种新的方法。我们还计算了给定阶的阿贝尔群的最小对称交叉帽数，并解决了作用于不可定向黎曼曲面上的阿贝尔群的最大阶问题。

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Abelian actions on compact nonorientable Riemann surfaces

Abstract Given an integer $g>2$ , we state necessary and sufficient conditions for a finite Abelian group to act as a group of automorphisms of some compact nonorientable Riemann surface of genus g. This result provides a new method to obtain the symmetric cross-cap number of Abelian groups. We also compute the least symmetric cross-cap number of Abelian groups of a given order and solve the maximum order problem for Abelian groups acting on nonorientable Riemann surfaces.

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来源期刊

Glasgow Mathematical Journal 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics. The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.