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http://hdl.handle.net/10662/16380
Title: | Genus zero of projective symplectic groups |
Authors: | Mohammed Salih, H.M. Hussein, Rezhna M. |
Keywords: | Grupo simpléctico;Punto fijo;Género cero;Symplectic group;Fixed point;Genus zero group |
Issue Date: | 2022 |
Publisher: | Universidad de Extremadura, Servicio de Publicaciones |
Abstract: | A transitive subgroup G ≤ SN is called a genus zero group if there exist non identity elements x1 , . . . , xr∈G satisfying G =<x1, . . . , xr>, x1·...·xr=1 and ind x1+...+ind xr = 2N − 2. The Hurwitz space Hinr(G) is the space of genus zero coverings of the Riemann sphere P1 with r branch points and the monodromy group G. In this paper, we assume that G is a finite group with PSp(4, q) ≤ G ≤ Aut(PSp(4, q)) and G acts on the projective points of 3-dimensional projective geometry PG(3, q), q is a prime power. We show that G possesses no genus zero group if q > 5. Furthermore, we study the connectedness of the Hurwitz space Hinr(G) for a given group G and q ≤ 5. |
URI: | http://hdl.handle.net/10662/16380 |
ISSN: | 0213-8743 |
DOI: | 10.17398/2605-5686.37.2.195 |
Appears in Collections: | Extracta Mathematicae Vol. 37, nº 2 (2022) |
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2605-5686_37_2_195.pdf | 387,98 kB | Adobe PDF | View/Open |
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