Abelian actions on compact bordered Klein surfaces

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• 作者：Jesús Rodríguez Martín de los Santos
• 关键词：Compact bordered surface ; Klein surface ; Automorphism group ; Real genus
• 刊名：Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：1
• 页码：189-204
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer Milan
• ISSN：1579-1505
• 卷排序：111

文摘

We state necessary and sufficient conditions for a finite abelian group to act as a group of automorphisms of some compact bordered Klein surface of algebraic genus \(p>1\). This result provides a new method to obtain the real genus, as well as solve the maximum order problem, of abelian groups. We also compute the least real genus of abelian groups of the same order.