2023-11-29T00:00:04Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/453232023-08-08T08:54:33Zcom_20.500.14352_14col_20.500.14352_21
A survey on the minimum genus and maximum order problems for bordered Klein surfaces
Bujalance, E.
Etayo Gordejuela, J. Javier
Gromadzki, G.
Campbell, C. M.
517.53
Klein surfaces
Functions of a complex variable
Funciones (Matemáticas)
1202 Análisis y Análisis Funcional
Every finite group acts as a group of automorphisms of some compact bordered Klein surface of algebraic genus g≥2 . The same group G may act on different genera and so it is natural to look for the minimum genus on which G acts. This is the minimum genus problem for the group G . On the other hand, for a fixed integer g≥2 , there are finitely many abstract groups acting as a group of automorphisms of some compact bordered Klein surface of algebraic genus g . The condition g≥2 assures that all such groups are finite. So it makes sense to look for the largest order of groups G acting on some surface of genus g when g is fixed and G runs over a prescribed family F of groups. This is the maximum order problem for the family F . There is a significant amount of research dealing with these two problems (or with some of their variations), and the corresponding results are scattered in the literature. The purpose of this survey is to gather some of these results, paying special attention to important families of finite groups
Depto. de Álgebra, Geometría y Topología
Fac. de Ciencias Matemáticas
TRUE
pub
2023-06-20T05:44:13Z
2023-06-20T05:44:13Z
2011
book part
https://hdl.handle.net/20.500.14352/45323
9780521279031
London Mathematical Society Lecture Note Series
metadata only access
Cambridge University Press