scholarly journals On automorphism groups of Riemann double covers of Klein surfaces

2017 ◽  
Vol 472 ◽  
pp. 146-171
Author(s):  
E. Bujalance ◽  
F.J. Cirre ◽  
M.D.E. Conder
Keyword(s):  
Automorphism Groups ◽  
Klein Surfaces ◽  
Double Covers

Automorphism Groups of Compact Bordered Klein Surfaces

1990 ◽  
Author(s):  
Emilio Bujalance ◽  
José Javier Etayo ◽  
José Manuel Gamboa ◽  
Grzegorz Gromadzki
Keyword(s):  
Automorphism Groups ◽  
Klein Surfaces

scholarly journals Automorphism groups of complex doubles of Klein surfaces

1994 ◽  
Vol 36 (3) ◽  
pp. 313-330 ◽  
Author(s):  
E. Bujalance ◽  
A. F. Costa ◽  
G. Gromadzki ◽  
D. Singerman
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Automorphism Groups ◽  
Natural Question ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Maximal Symmetry ◽  
Group Of Automorphisms

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+).

scholarly journals On the order of automorphism groups of Klein surfaces

1985 ◽  
Vol 26 (1) ◽  
pp. 75-81 ◽  
Author(s):  
J. J. Etayo Gordejuela
Keyword(s):  
General Result ◽  
Special Interest ◽  
Riemann Surfaces ◽  
Prime Order ◽  
Automorphism Groups ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Group Of Automorphisms

A problem of special interest in the study of automorphism groups of surfaces are the bounds of the orders of the groups as a function of the genus of the surface.May has proved that a Klein surface with boundary of algebraic genus p has at most 12(p–1) automorphisms [9].In this paper we study the highest possible prime order for a group of automorphisms of a Klein surface. This problem was solved for Riemann surfaces by Moore in [10]. We shall use his results for studying the Klein surfaces that are not Riemann surfaces. The more general result that we obtain is the following: if X is a Klein surface of algebraic genus p, and G is a group of automorphisms of X, of prime order n, then n ≤ p + 1.

scholarly journals Large automorphism groups of compact Klein surfaces with boundary, I

1977 ◽  
Vol 18 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Coy L. May
Keyword(s):  
Automorphism Groups ◽  
Klein Surface ◽  
Klein Surfaces

LetXbe a Klein surface [1], that is,Xis a surface with boundary მXtogether with a dianalytic structure onX. A homeomorphismf:X→XofXonto itself that is dianalytic will be called anautomorphismofX.

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