Geodesic
A Note on Regular Coverings of Closed Orientable Surfaces
Glasgow mathematical journal, Tome 5 (1961) no. 2, pp. 49-66

Voir la notice de l'article provenant de la source Cambridge University Press

The object of this note is to study the regular coverings of the closed orientable surface of genus 2.Let the closed orientable surface Fh of genus h be a covering of F2 and let and f be the fundamental groups respectively. Then is a subgroup of f of index n = h − 1. A covering is called regular if is normal in f.Conversely, let be a normal subgroup of f of finite index. Then there is a uniquely determined regular covering Fh such that is the fundamental group of Fh. The covering Fh is an orientable surface. Since the index n of in f is supposed to be finite, Fh is closed, and its genus is given by n = h − 1.The fundamental group f can be defined by. 
A Note on Regular Coverings of Closed Orientable Surfaces. Glasgow mathematical journal, Tome 5 (1961) no. 2, pp. 49-66. doi: 10.1017/S2040618500034316
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[1] 1.Bachmann, F., Aufbau der Geometrie aus dem Spiegelungsbegriff (Heidelberg, 1959). Google Scholar | DOI

[2] 2.Bergau, P. and Mennicke, J., Über topologische Abbildungen der Brezelfläche vom Geschlecht 2, Math. Zeit. 74 (1960), 414–435. Google Scholar | DOI

[3] 3.Brenner, J. L., The linear homogeneous group, Ann. of Math. 39 (1938), 472–493. Google Scholar | DOI

[4] 4.Brenner, J. L., The linear homogeneous group, II, Ann. of Math. 45 (1944), 101–109. Google Scholar | DOI

[5] 5.Brenner, J. L., The linear homogeneous group, III, Ann. of Math. 71 (1960), 210–223. Google Scholar | DOI

[6] 6.Coxeter, H. S. M. and Moser, J., Generators and relations for discrete groups (Erg. d. Math., N. F. 14, 1957). Google Scholar | DOI

[7] 7.Dickson, L. E., Linear groups, with an exposition of the Galois field theory (New York, 1958). Google Scholar

[8] 8.Fenchel, W., On the projective geometric foundations of the non-Euclidean geometry, Mat. Tidsskr. B. 1941, 18–30 (Danish). Google Scholar

[9] 9.Goeritz, L., Die Abbildungen der Brezelfläche und der Vollbrezel vom Geschlecht 2, Hamb. Abh. 9 (1933), 244–259. Google Scholar | DOI

[10] 10.Jones, B. W., The arithmetic theory of quadratic forms (New York, 1950). Google Scholar | DOI

[11] 11.Klein, F., Elementary mathematics from an advanced standpoint—Geometry (New York, 1939). Google Scholar

[12] 12.Reiner, I., Normal subgroups of the unimodular group, Illinois J. Math. 2 (1958), 142–144. Google Scholar | DOI

[13] 13.Seifert, H. and Threlfall, W., Lehrbuch der Topologie (New York, 1947). Google Scholar

[14] 14.Waerden, B. L. Van der, Gruppen von linearen Transformationen (Erg. d. Math. 4, 1935). Google Scholar | DOI

[15] 15.Zassenhaus, H., The theory of groups (New York, 2nd ed. 1958). Google Scholar

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