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Abstract
The Hurwitz space is the space of genus g covers of the Riemann sphere with branch points and the monodromy group . In this paper, we enumerate the connected components of the Hurwitz spaces for a finite primitive group of degree 7 and genus zero except . We achieve this with the aid of the computer algebra system GAP and the MAPCLASS package.
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References
- Michael, D.F. and Helmut, V. The inverse Galois problem and rational points on moduli spaces. Mathematische Annalen, 1991, 290(4), 771-800.
- Daniel, F., Robert, G. and Kay, M. Genus 0 actions of groups of Lie rank 1. American Mathematical Society, Providence, Rhode Island, Proceedings of Symposia in Pure Mathematics, 2002,70, 449-483.
- Daniel, F. and Kay, M. Composition factors of monodromy groups. Annals of Mathematics. Second Series. 2001, 154(2), 327-345.
- The GAP Group. GAP-Groups, Algorithms, and Programming, Version 4.6.2, 2013. http://www.gap-system.org
- Wang, G. Genus Zero Systems for Primitive Groups of Affine Type. 2011. Ph.D Thesis University of Birmingham, UK.
- Robert, M.G. and John, G.T. Finite groups of genus zero. Journal of Algebra, 1990, 131(1), 303-341.
- Magaard, K., Shpectorov, S. and Wang, G. Generating sets of affine groups of low genus. In Computational algebraic and analytic geometry, American Mathematical Society, Providence, Rhode Island, 2012, 572, 173-192.
- Haval, M.S. Finite Groups of Small Genus. 2014. Ph.D Thesis University of Birmingham, UK.
- Michael, G.N. On solvable monodromy groups of fixed genus. Pro-Quest LLC, Ann Arbor, Michigan, 1989. Ph.D Thesis University of Southern California, USA.
- Helmut, V. Groups as Galois groups an introduction, Volume 53, Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1996.
References
Michael, D.F. and Helmut, V. The inverse Galois problem and rational points on moduli spaces. Mathematische Annalen, 1991, 290(4), 771-800.
Daniel, F., Robert, G. and Kay, M. Genus 0 actions of groups of Lie rank 1. American Mathematical Society, Providence, Rhode Island, Proceedings of Symposia in Pure Mathematics, 2002,70, 449-483.
Daniel, F. and Kay, M. Composition factors of monodromy groups. Annals of Mathematics. Second Series. 2001, 154(2), 327-345.
The GAP Group. GAP-Groups, Algorithms, and Programming, Version 4.6.2, 2013. http://www.gap-system.org
Wang, G. Genus Zero Systems for Primitive Groups of Affine Type. 2011. Ph.D Thesis University of Birmingham, UK.
Robert, M.G. and John, G.T. Finite groups of genus zero. Journal of Algebra, 1990, 131(1), 303-341.
Magaard, K., Shpectorov, S. and Wang, G. Generating sets of affine groups of low genus. In Computational algebraic and analytic geometry, American Mathematical Society, Providence, Rhode Island, 2012, 572, 173-192.
Haval, M.S. Finite Groups of Small Genus. 2014. Ph.D Thesis University of Birmingham, UK.
Michael, G.N. On solvable monodromy groups of fixed genus. Pro-Quest LLC, Ann Arbor, Michigan, 1989. Ph.D Thesis University of Southern California, USA.
Helmut, V. Groups as Galois groups an introduction, Volume 53, Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1996.