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In this work we give pairs of generators (x, y) for the alternating groups An, 5 ? n ? 19, such that they determine the minimal genus of a Riemann surface on which An acts as the automorphism group. Using these results we prove that A15 is the u[...]texto impreso
The authors obtain the pairs of generators, necessary to study the non-orientable case, of the alternating groups $A_n$ for 21, 22, 28 and 29, which are also Hurwitz groups, groups with maximal number of automorphisms on Riemann surfaces[...]texto impreso
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Bujalance, E. ; Etayo Gordejuela, J. Javier | Department of Mathematics, Tokyo Institute of Technology | 1987If G is a group of automorphisms of a hyperelliptic Riemann surface of genus g represented as D/$\Gamma$ where D is the hyperbolic plane and $\Gamma$ a Fuchsian group, then $G\cong \Gamma '/\Gamma$ where $\Gamma$ ' is also a Fuchsian group. Furt[...]texto impreso
Bujalance, E. ; Etayo Gordejuela, J. Javier ; Gamboa, J. M. | Universidad Complutense de Madrid | 1986The authors describe in terms of non-Euclidean crystallographic groups all Klein surfaces whose automorphism group is one of the following: Z/p???Z/p , Z/pq , or Z/p 2 , where p and q are distinct odd primes. This includes every nontrivial fi[...]texto impreso
Let C be an algebraic curve of genus 3, defined over the real field R. The automorphism group of C is studied in this paper. In a paper by the same authors [Mich. Math. J. 33, 55-74 (1986; see 20043 below)], the hyperelliptic case was solved, th[...]texto impreso
A compact Klein surface with boundary of algebraic genus g?2 has at most 12(g?1) automorphisms. When a surface attains this bound we say that it has maximal symmetry, and the group of automorphisms is then an M group. In this paper we exhibit fo[...]texto impreso
A compact Klein surface X is called q-hyperelliptic if there is an involution $\phi$ of X such that the quotient surface $X/ $ has algebraic genus q. If X is represented as D/$\Gamma$ where D is the unit disc and $\Gamma$ a non-Euclidean crysta[...]texto impreso
Bujalance, E. ; Etayo Gordejuela, J. Javier ; Gamboa, J. M. | Real Academia de Ciencias Exactas, Físicas y Naturales | 1984The classical correspondence between Riemann surfaces and complex algebraic curves, extends by the work of Ailing and Greenleaf to Klein surfaces and real algebraic curves. The topological invariants of the surface determine the ones of a smonot[...]texto impreso
Elliptic-hyperelliptic, normal, unramified, double coverings of bordered hyperelliptic Klein surfaces are considered here, using methods of the theory on non-Euclidean crystallographic groups. Complete proofs will appear elsewheretexto impreso
Todo grupo finito G actúa como grupo de automorfismos de diversas superficies de Klein con borde. Al menor de los géneros algebraicos de estas superficies se le llama género real ?(G) del grupo G. Se conocen todos los grupos con0 ? ?(G) ? 8, as?[...]texto impreso
Castrillón López, Marco ; Díaz-Cano Ocaña, Antonio ; Etayo Gordejuela, J. Javier ; Folgueira, Marta ; Infante del Río, Juan Antonio ; Pozo Coronado, Luis Miguel ; Rey Cabezas, Jose María | No publicado | 2013Material elaborado por profesores de la UCM para la asignatura de este nombre del grado en Ingeniería Matemáticas, el grado en Matemáticas y el grado en Matemáticas y Estadística. Contenidos: - Números enteros. Dígitos de control y criptografía[...]texto impreso
The authors establish that an elliptic-hyperelliptic Klein surface of genus p > 5 generically has at most 4(p-1)automorphisms, excepting the case X is orientable with 2 or 4 boundary components. If X is orientable with 2 or 4 boundary componen[...]texto impreso
En el polígono hiperbólico con todos los águlos rectos, se obtienen fórmulas explícitas parael coseno y el seno y el seno hiperbólicos de la longitud de un lado l en función de las longintudes de los N-3 lados dictintos a l y a sus adyacentes. T[...]
