Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T14:01:17.778Z Has data issue: false hasContentIssue false
  • English
  • Français

FROBENIUS GROUPS AS MONODROMY GROUPS

Part of: Permutation groups Curves

Published online by Cambridge University Press:  01 October 2008

ROBERT M. GURALNICK
ROBERT M. GURALNICK*
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study Frobenius groups acting on curves.

Keywords

Frobenius groupmonodromy groupcoverings of curves

MSC classification

Secondary: 14H30: Coverings, fundamental group 14H05: Algebraic functions; function fields 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 2 , October 2008 , pp. 191 - 196
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Flynn, John, ‘Near-exceptionality over finite fields’, PhD Thesis, University of California Berkeley, 2001.Google Scholar
[2]Guralnick, Robert M., ‘Rational functions with monodromy group a Frobenius group’, Preprint, 2000.Google Scholar
[3]Guralnick, Robert M., ‘Solvable monodromy groups of low genus covers’, Preprint.Google Scholar
[4]Guralnick, Robert M., Monodromy Groups of Coverings of Curves, Galois Groups and Fundamental Groups, Mathematical Sciences Research Institute Publications, 41 (Cambridge University Press, Cambridge, 2003), pp. 1–46.Google Scholar
[5]Guralnick, Robert M., Müller, Peter and Saxl, Jan, ‘The rational function analogue of a question of Schur and exceptionality of permutation representations’, Mem. Amer. Math. Soc. 162(773) (2003).Google Scholar
[6]Silverman, Joseph H., The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 106 (Springer, New York, 1992).Google Scholar
[7]Thompson, J. G., ‘Finite groups with fixed-point-free automorphisms of prime order’, Proc. Natl. Acad. Sci. USA 45 (1959), 578–581.CrossRefGoogle ScholarPubMed