Genus zero of projective symplectic groups
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 po...
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| Format: | Article |
| Language: | English |
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University of Extremadura
2022-07-01
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| Series: | Extracta Mathematicae |
| Subjects: | |
| Online Access: | https://publicaciones.unex.es/index.php/EM/article/view/1359 |
| _version_ | 1818488330257432576 |
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| author | H.M Mohammed Salih Rezhna M. Rezhna M. Hussein |
| author_facet | H.M Mohammed Salih Rezhna M. Rezhna M. Hussein |
| author_sort | H.M Mohammed Salih |
| collection | DOAJ |
| description |
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.
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| first_indexed | 2024-12-10T16:49:41Z |
| format | Article |
| id | doaj.art-d95fb38d8dd946fea32a032cf77a1146 |
| institution | Directory Open Access Journal |
| issn | 0213-8743 2605-5686 |
| language | English |
| last_indexed | 2024-12-10T16:49:41Z |
| publishDate | 2022-07-01 |
| publisher | University of Extremadura |
| record_format | Article |
| series | Extracta Mathematicae |
| spelling | doaj.art-d95fb38d8dd946fea32a032cf77a11462022-12-22T01:40:57ZengUniversity of ExtremaduraExtracta Mathematicae0213-87432605-56862022-07-01Genus zero of projective symplectic groupsH.M Mohammed Salih0Rezhna M. Rezhna M. Hussein1Department of Mathematics, Faculty of Science, Soran University Kawa St. Soran, Erbil, IraqDepartment of Mathematics, Faculty of Science, Soran University Kawa St. Soran, Erbil, Iraq 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. https://publicaciones.unex.es/index.php/EM/article/view/1359symplectic groupfixed pointgenus zero group |
| spellingShingle | H.M Mohammed Salih Rezhna M. Rezhna M. Hussein Genus zero of projective symplectic groups Extracta Mathematicae symplectic group fixed point genus zero group |
| title | Genus zero of projective symplectic groups |
| title_full | Genus zero of projective symplectic groups |
| title_fullStr | Genus zero of projective symplectic groups |
| title_full_unstemmed | Genus zero of projective symplectic groups |
| title_short | Genus zero of projective symplectic groups |
| title_sort | genus zero of projective symplectic groups |
| topic | symplectic group fixed point genus zero group |
| url | https://publicaciones.unex.es/index.php/EM/article/view/1359 |
| work_keys_str_mv | AT hmmohammedsalih genuszeroofprojectivesymplecticgroups AT rezhnamrezhnamhussein genuszeroofprojectivesymplecticgroups |