Klein surfaces with maximal symmetry and their groups of automorphisms

1984 ◽  
Vol 268 (4) ◽  
pp. 533-538 ◽  
Author(s):  
J. J. Etayo Gordejuela
Keyword(s):  
Klein Surfaces ◽  
Maximal Symmetry ◽  
Groups Of Automorphisms

scholarly journals Complex doubles of bordered Klein surfaces with maximal symmetry

1991 ◽  
Vol 33 (1) ◽  
pp. 61-71 ◽  
Author(s):  
Coy L. May
Keyword(s):  
Automorphism Group ◽  
Special Interest ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Maximal Symmetry

A compact bordered Klein surface X of algebraic genus g ≥ 2 has maximal symmetry [6] if its automorphism group A(X) is of order 12(g — 1), the largest possible. The bordered surfaces with maximal symmetry are clearly of special interest and have been studied in several recent papers ([6] and [9] among others).

Groups acting on bordered Klein surfaces with maximal symmetry

2003 ◽  
pp. 50-58 ◽  
Author(s):  
Emilio Bujalance ◽  
Francisco Javier Cirre ◽  
Peter Turbek
Keyword(s):  
Klein Surfaces ◽  
Maximal Symmetry

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

scholarly journals Orientable and non-orientable Klein surfaces with maximal symmetry

1985 ◽  
Vol 26 (1) ◽  
pp. 31-34 ◽  
Author(s):  
David Singerman
Keyword(s):  
Finite Group ◽  
Upper Bound ◽  
Closed Surface ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Maximal Symmetry ◽  
Group Of Automorphisms ◽  
G 12 ◽  
Image Position ◽  
A Finite Group

Let X be a bordered Klein surface, by which we mean a Klein surface with non-empty boundary. X is characterized topologically by its orientability, the number k of its boundary components and the genus p of the closed surface obtained by filling in all the holes. The algebraic genus g of X is defined by.If g≥2 it is known that if G is a group of automorphisms of X then |G|≤12(g-l) and that the upper bound is attained for infinitely many values of g ([4], [5]). A bordered Klein surface for which this upper bound is attained is said to have maximal symmetry. A group of 12(g-l) automorphisms of a bordered Klein surface of algebraic genus g is called an M*-group and it is known that a finite group G is an M*-group if and only if it is generated by 3 non-trivial elements T1, T2, T3 which obey the relations([4]).

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+).

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