Cyclic groups of automorphisms of compact Klein surfaces

1990 ◽  
pp. 60-97
Author(s):  
Emilio Bujalance ◽  
José Javier Etayo ◽  
José Manuel Gamboa ◽  
Grzegorz Gromadzki
Keyword(s):  
Klein Surfaces ◽  
Cyclic Groups ◽  
Groups Of Automorphisms

scholarly journals Groups of automorphisms of hyperelliptic Klein surfaces of genus three.

1986 ◽  
Vol 33 (1) ◽  
pp. 55-74 ◽  
Author(s):  
E. Bujalance ◽  
J. J. Etayo ◽  
J. M. Gamboa
Keyword(s):  
Klein Surfaces ◽  
Groups Of Automorphisms

On the Monodromy Groups of Riemann Surfaces of Genus ≧1

1981 ◽  
Vol 33 (5) ◽  
pp. 1142-1156
Author(s):  
Kathryn Kuiken
Keyword(s):  
Finite Group ◽  
Riemann Surface ◽  
Riemann Surfaces ◽  
Abelian Groups ◽  
General Question ◽  
Group Of Automorphisms ◽  
Cyclic Groups ◽  
Monodromy Groups ◽  
Groups Of Automorphisms ◽  
A Finite Group

It is well-known [5, 19] that every finite group can appear as a group of automorphisms of an algebraic Riemann surface. Hurwitz [9, 10] showed that the order of such a group can never exceed 84 (g – 1) provided that the genus g is ≧2. In fact, he showed that this bound is the best possible since groups of automorphisms of order 84 (g – 1) are obtainable for some surfaces of genus g. The problems considered by Hurwitz and others can be considered as particular cases of a more general question: Given a finite group G, what is the minimum genus of the surface for which it is a group of automorphisms? This question has been completely answered for cyclic groups by Harvey [7]. Wiman's bound 2(2g + 1), the best possible, materializes as a consequence. A further step was taken by Maclachlan who answered this question for non-cyclic Abelian groups.

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