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Automorphism groups of complex doubles of Klein surfaces

Published online by Cambridge University Press:  18 May 2009

E. Bujalance ,
A. F. Costa ,
G. Gromadzki  and
D. Singerman
E. Bujalance
Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, Madrid 28040, Spain
A. F. Costa
Affiliation:
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, Madrid 28040, Spain
G. Gromadzki
Affiliation:
Institute of Mathematics, WSP, Chodkiewicza 30, 85-064, Bydgoszcz, Poland
D. Singerman
Affiliation:
Faculty of Mathematical Studies, The University, Southampton SO9 5NH, UK
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In this paper we consider complex doubles of compact Klein surfaces that have large automorphism groups. It is known that a bordered Klein surface of algebraic genus g > 2 has at most 12(g − 1) automorphisms. Surfaces for which this bound is sharp are said to have maximal symmetry. The complex double of such a surface X is a compact Riemann surface X+ of genus g and it is easy to see that if G is the group of automorphisms of X then C2 × G is a group of automorphisms of X+. A natural question is whether X+ can have a group that strictly contains C2 × G. In [8] C. L. May claimed the following interesting result: there is a unique Klein surface X with maximal symmetry for which Aut X+ properly contains C2 × Aut X (where Aut X+ denotes the group of conformal and anticonformal automorphisms of X+).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 313 - 330
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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