Small Mathieu group coverings in characteristic two
HTML articles powered by AMS MathViewer
- by Shreeram S. Abhyankar and Ikkwon Yie PDF
- Proc. Amer. Math. Soc. 123 (1995), 1319-1329 Request permission
Abstract:
Explicit equations are given for unramified coverings of the affine line in characteristic two whose Galois groups are the Mathieu groups of degrees 11 and 12 and the automorphism group of the Mathieu group of degree 12.References
- Shreeram Abhyankar, Coverings of algebraic curves, Amer. J. Math. 79 (1957), 825–856. MR 94354, DOI 10.2307/2372438
- Shreeram Shankar Abhyankar, Resolution of singularities of embedded algebraic surfaces, Pure and Applied Mathematics, Vol. 24, Academic Press, New York-London, 1966. MR 0217069
- Shreeram S. Abhyankar, Desingularization of plane curves, Singularities, Part 1 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 1–45. MR 713043
- Shreeram S. Abhyankar, Algebraic geometry for scientists and engineers, Mathematical Surveys and Monographs, vol. 35, American Mathematical Society, Providence, RI, 1990. MR 1075991, DOI 10.1090/surv/035
- Shreeram S. Abhyankar, Galois theory on the line in nonzero characteristic, Bull. Amer. Math. Soc. (N.S.) 27 (1992), no. 1, 68–133. MR 1118002, DOI 10.1090/S0273-0979-1992-00270-7
- Shreeram S. Abhyankar, Mathieu group coverings in characteristic two, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 3, 267–271 (English, with English and French summaries). MR 1205196, DOI 10.2307/2161167
- Shreeram S. Abhyankar, Alternating group coverings of the affine line for characteristic greater than two, Math. Ann. 296 (1993), no. 1, 63–68. MR 1213371, DOI 10.1007/BF01445094
- Shreeram S. Abhyankar, Fundamental group of the affine line in positive characteristic, Geometry and analysis (Bombay, 1992) Tata Inst. Fund. Res., Bombay, 1995, pp. 1–26. MR 1351500
- Shreeram S. Abhyankar, Wreath products and enlargements of groups, Discrete Math. 120 (1993), no. 1-3, 1–12. MR 1235890, DOI 10.1016/0012-365X(93)90560-G
- Shreeram S. Abhyankar, William Heinzer, and Paul Eakin, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra 23 (1972), 310–342. MR 306173, DOI 10.1016/0021-8693(72)90134-2
- Shreeram S. Abhyankar, Jun Ou, and Avinash Sathaye, Alternating group coverings of the affine line for characteristic two, Discrete Math. 133 (1994), no. 1-3, 25–46. MR 1298962, DOI 10.1016/0012-365X(94)90014-0
- Shreeram S. Abhyankar and Ikkwon Yie, Small degree coverings of the affine line in characteristic two, Discrete Math. 133 (1994), no. 1-3, 1–23. MR 1298961, DOI 10.1016/0012-365X(94)90013-2
- Shreeram S. Abhyankar and Ikkwon Yie, Some more Mathieu group coverings in characteristic two, Proc. Amer. Math. Soc. 122 (1994), no. 4, 1007–1014. MR 1239794, DOI 10.1090/S0002-9939-1994-1239794-1
- Bertram Huppert and Norman Blackburn, Finite groups. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 242, Springer-Verlag, Berlin-New York, 1982. AMD, 44. MR 650245 E. Mathieu, Mémoire sur l’étude des fonctions de plusieurs quantités, sur la manière de les former, et sur les substitutions qui les laissent invariables, J. Math Pures Appl. 18 (1861), 241-323. G. A. Miller, List of transitive substitution groups of degree twelve, Quart. J. Pure Appl. Math. 28 (1896), 193-231.
- Michio Suzuki, Gun ron. Vol. 1, Gendai Sūgaku [Modern Mathematics], vol. 18, Iwanami Shoten, Tokyo, 1977 (Japanese). MR 514842
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1319-1329
- MSC: Primary 14H30; Secondary 14E22, 14H25
- DOI: https://doi.org/10.1090/S0002-9939-1995-1246511-9
- MathSciNet review: 1246511