The full group of automorphisms of non-orientable unbordered Klein surfaces of topological genus 3, 4 and 5

被引：0
作者：
E. Bujalance
J. J. Etayo
E. Martínez
机构：
[1] UNED,Departamento de Matemáticas Fundamentales
[2] Universidad Complutense,Departamento de Álgebra, Facultad de Matemáticas
来源：
Revista Matemática Complutense | 2014年 / 27卷
关键词：
Non-orientable surface; Klein surface; Automorphism group; Symmetric crosscap number; Primary 57M60; Secondary 20F05; 20H10; 30F50;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
An important problem in the study of Riemann and Klein surfaces is determining their full automorphism groups. Up to now only very partial results are known, concerning surfaces of low genus or families of surfaces with special properties. This paper deals with non-orientable unbordered Klein surfaces. In this case the solution of the problem is known for surfaces of genus 1 and 2, and for hyperelliptic surfaces. Here we explicitly obtain the full automorphism group of all surfaces of genus 3, 4 and 5.
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页码：305 / 326
页数：21
相关论文
共 35 条
[1]  
Bujalance E(1982)Normal NEC signatures Ill. J. Math. 26 519-530
[2]  
Bujalance E(1983)Cyclic groups of automorphisms of compact non-orientable Klein surfaces without boundary Pac. J. Math. 109 279-289
[3]  
Bujalance E(2003)On extendability of group actions on compact Riemann surfaces Trans. Am. Math. Soc. 355 1537-1557
[4]  
Cirre FJ(2010)Finite group actions on bordered surfaces of small genus J. Pure Appl. Algebra. 214 2165-2185
[5]  
Conder MDE(2001)Determination of all regular maps of small genus J. Comb. Theory Ser. B 81 224-242
[6]  
Bujalance E(1939)The abstract groups Trans. Am. Math. Soc. 45 73-150
[7]  
Cirre FJ(1923)Abstract group definitions and applications Trans. Am. Math. Soc. 25 193-210
[8]  
Conder MDE(2006)Non-normal pairs of non-Euclidean crystallographic groups Bull. Lond. Math. Soc. 38 113-123
[9]  
Szepietowski B(2008)The symmetric crosscap number of the groups $$C_{m}\times D_{n}$$ Proc. R. Soc. Edinb. 138 1197-1213
[10]  
Conder MDE(2011)The action of the groups Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 105 97-108
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