Geodesic
Minimum topological genus of compact bordered Klein surfaces admitting a prime-power automorphism
Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 221-232

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

In the nineteenth century, Hurwitz [8] and Wiman [14] obtained bounds for the order of the automorphism group and the order of each automorphism of an orientable and unbordered compact Klein surface (i. e., a compact Riemann surface) of topological genus g s 2. The corresponding results of bordered surfaces are due to May, [11], [12]. These may be considered as particular cases of the general problem of finding the minimum topological genus of a surface for which a given finite group G is a group of automorphisms. This problem was solved for cyclic and abelian G by Harvey [7] and Maclachlan [10], respectively, in the case of Riemann surfaces and by Bujalance [2], Hall [6] and Gromadzki [5] in the case of non-orientable and unbordered Klein surfaces. In dealing with bordered Klein surfaces, the algebraic genus—i. e., the topological genus of the canonical double covering, (see Alling-Greenleaf [1])—was minimized by Bujalance- Etayo-Gamboa-Martens [3] in the case where G is cyclic and by McCullough [13] in the abelian case. 
Bujalance, E.; Gamboa, J. M.; Maclachlan, C. Minimum topological genus of compact bordered Klein surfaces admitting a prime-power automorphism. Glasgow mathematical journal, Tome 37 (1995) no. 2, pp. 221-232. doi: 10.1017/S0017089500031128
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