Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Galois groups over function fields of positive characteristic

Author(s): John Conway; John McKay; Allan Trojan
Journal: Proc. Amer. Math. Soc. 138 (2010), 1205-1212.
MSC (2000): Primary 11F22, 11F03; Secondary 30F35, 20C34
Posted: November 20, 2009
MathSciNet review: 2578514
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We prove examples motivated by work of Serre and Abhyankar.

References:

1.: Abhyankar, S. ``Coverings of algebraic curves'', Amer. J. Math., 79, 825-856, 1957. MR 0094354 (20:872)
2.: Abhyankar, S. ``Galois theory on the line in nonzero characteristic'', Bull. Amer. Math. Soc. (N.S.), 27, no. 1, pp. 68-133, 1992. MR 1118002 (94a:12004)
3.: Abhyankar, S. ``Mathieu group coverings in characteristic two'', Comptes Rendus Sci. Paris Sér. I. Math., 316, no. 3, pp. 267-271, 1993. MR 1205196 (94g:14013)
4.: Abhyankar, S. ``Resolution of singularities and modular Galois theory'', Bull. Amer. Math. Soc. (N.S.) 38, no. 2, pp. 131-169 (electronic), 2001. MR 1816069 (2002a:14013)
5.: Abhyankar, S., Yie, I. ``Small degree coverings of the affine line in characteristic two'', Discrete Math., 133, pp. 1-23, 1994. MR 1298961 (95h:14017)
6.: ``Algorithmic Methods in Galois Theory'', J. Symb. Comp., 30, Elsevier, pp. 635-872, 2000. MR 1800030 (2001f:12001)
7.: ``Atlas of Finite Group Representations'', brauer.maths.qmul.ac.uk/Atlas/v3.
8.: Casperson, D., McKay, J., ``Symmetric functions, -sets and Galois groups'', Math. Comp., 63, pp. 749-757, 1994. MR 1234424 (95a:12001)
9.: Conway, J., McKay, J., `` $M_{24}$ is the Galois group over of $x^{24} + x + t$ '', Mathematical Abstracts, Amer. Math. Soc., 93T-12-69, p. 391, 1993.
10.: MacWilliams, F.J., Sloane, N.J.A., ``The Theory of Error-Correcting Codes. I'', North Holland, p. 70, 1977. MR 0465509 (57:5408a)
11.: van der Waerden, B.L., ``Algebra, Vol. 1'', Frederick Ungar Publishing Co., 8.10, 1970. MR 263582 (41:8187a)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11F22, 11F03, 30F35, 20C34

Retrieve articles in all Journals with MSC (2000): 11F22, 11F03, 30F35, 20C34

Additional Information:

John Conway
Affiliation: Department of Mathematics, Fine Hall, Princeton University, Washington Road, Princeton, New Jersey 08544-1000
Email: conway@math.princeton.edu

John McKay
Affiliation: Department of Mathematics and CICMA, Concordia University, 1455 de Maisonneuve Boulevard, West, Montreal, Quebec H3G 1M8, Canada
Email: mac@mathstat.concordia.ca

Allan Trojan
Affiliation: Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada
Email: atrojan@yorku.ca

DOI: 10.1090/S0002-9939-09-10130-2
PII: S 0002-9939(09)10130-2
Keywords: Galois groups, Mathieu groups, function fields
Received by editor(s): November 25, 2008,
Received by editor(s) in revised form: July 27, 2009
Posted: November 20, 2009
Communicated by: Jonathan I. Hall
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|