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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
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
Pieren Pidal, Agustín Pedro ; Areces, J.L. ; Toraño, J. ; Martínez García, Ernesto | Universidad Complutense de Madrid. Departamento de Estratigraf?a | 1995Una campaña de investigación geológico-minera del yacimiento carbonífero de «Mina La Camocha» ha aportado nuevos y abundantes datos del Pérmico de la Orla Cantábrica. Al no aflorar en ningún punto el Carbonífero investigado con fines mineros, se[...]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[...]texto impreso
Etayo Gordejuela, J. Javier ; Martínez García, Ernesto | Matematisk Institut, Universitetsparken NY Munkegade | 2004We construct a special type of fundamental regions for any Fuchsian group $F$ generated, by an even number of half-turns, and for certain non-Euclidean crystallographic groups (NEC groups in short). By comparing these regions we give geometrical[...]texto impreso
Etayo Gordejuela, J. Javier ; Gromadzki, G. ; Martínez García, Ernesto | BIRKHAUSER VERLAG AG | 2012In virtue of the Belyi Theorem an algebraic curve can be defined over the algebraic numbers if and only if the corresponding Riemann surface can be uniformized by a subgroup of a Fuchsian triangle group. Such surfaces are known as Belyi surfaces[...]texto impreso
The minimum genus problem consists in determining the minimum algebraic genus of a surface on which a viven group G acts. For cyclic groups G this problem on bordered Klein surfaces was solved in 1989. The next step is to fix the number of bound[...]texto impreso
Every finite group G may act as an automorphism group of Klein surfaces either bordered or unbordered either orientable or non-orientable. For each group the minimum genus receives different names according to the topological features of the sur[...]texto impreso
Every finite group G acts as an automorphism group of several bordered compact Klein surfaces. The minimal genus of these surfaces is called the real genus and denoted by ?(G). The systematical study was begun by C.L. May and continued by him in[...]texto impreso
A Klein surface with boundary of algebraic genus $\mathfrak{p}\geq 2$, has at most $12(\mathfrak{p}-1)$ automorphisms. The groups attaining this upper bound are called $M^{\ast}$-groups, and the corresponding surfaces are said to have maximal sy[...]texto impreso
Etayo Gordejuela, J. Javier ; Gromadzki, G. ; Martínez García, Ernesto | University of Houston | 2012Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric crosscap number and denoted by ?˜(G). The systematic study about the symmetric[...]texto impreso
Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric cross-cap number and denoted by ˜?(G). This number is related to other paramet[...]
