Connected Components of the Hurwitz Space for the Symmetric Group of Degree 7

Authors

Haval M. Mohammed Salih, Soran University, Faculty of Science, Mathematics Department-Kawa St, Soran, Erbil, Iraq
University of Raparian, College of Basic Education, Department of Mathematic, Ranya, Kurdistan Region of Iraq, University of Raparian, College of Basic Education, Department of Mathematic, Ranya, Kurdistan Region of Iraq

Abstract

The Hurwitz space is the space of genus covers of the Riemann sphere with branch points and the monodromy group . Let be the symmetric group . In this paper, we enumerate the connected components of . Our approach uses computational tools, relying on the computer algebra system GAP and the MAPCLASS package, to find the connected components of . This work gives us the complete classification of primitive genus zero symmetric group of degree seven.

Recommended Citation

Salih, Haval M. Mohammed and Iraq, University of Raparian, College of Basic Education, Department of Mathematic, Ranya, Kurdistan Region of (2019) Connected Components of the Hurwitz Space for the Symmetric Group of Degree 7, Sultan Qaboos University Journal For Science: Vol. 24: Iss. 2, 129-138.
DOI: https://doi.org/10.24200/squjs.vol24iss2pp129-138
Available at: https://squjs.squ.edu.om/squjs/vol24/iss2/1