Again nice equations for nice groups

Author:
Shreeram S. Abhyankar

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2967-2976

MSC (1991):
Primary 12F10, 14H30, 20D06, 20E22

MathSciNet review:
1343675

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Abstract | References | Similar Articles | Additional Information

Abstract: Nice quartinomial equations are given for unramified coverings

of the affine line in nonzero characteristic with PSU and

SU as Galois groups where is any integer and is any power of .

**[A01]**Shreeram Abhyankar,*Coverings of algebraic curves*, Amer. J. Math.**79**(1957), 825–856. MR**0094354****[A02]**Shreeram Abhyankar,*Tame coverings and fundamental groups of algebraic varieties. I. Branch loci with normal crossings; Applications: Theorems of Zariski and Picard*, Amer. J. Math.**81**(1959), 46–94. MR**0104675****[A03]**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**, 10.1090/S0273-0979-1992-00270-7**[A04]**S. S. Abhyankar,*Nice equations for nice groups*, Israel Journal of Mathematics**88**(1994), 1--24. CMP**95:04****[A05]**S. S. Abhyankar,*More nice equations for nice groups*, Proceedings of the American Mathematical Society**124**(1996), 3577--3591.**[Asc]**Michael Aschbacher,*Finite group theory*, Cambridge Studies in Advanced Mathematics, vol. 10, Cambridge University Press, Cambridge, 1986. MR**895134****[Dic]**L. E. Dickson,*Linear Groups*, Teubner, 1901.**[Li1]**Martin W. Liebeck,*The affine permutation groups of rank three*, Proc. London Math. Soc. (3)**54**(1987), no. 3, 477–516. MR**879395**, 10.1112/plms/s3-54.3.477**[Li2]**M. W. Liebeck,*Characterization of classical groups by orbit sizes on the natural module*, Proceedings of the American Mathematical Society**124**(1996), 3561--3566.**[LiK]**Peter Kleidman and Martin Liebeck,*The subgroup structure of the finite classical groups*, London Mathematical Society Lecture Note Series, vol. 129, Cambridge University Press, Cambridge, 1990. MR**1057341****[Tay]**Donald E. Taylor,*The geometry of the classical groups*, Sigma Series in Pure Mathematics, vol. 9, Heldermann Verlag, Berlin, 1992. MR**1189139****[PPS]**T. Penttila, C. E. Praeger and J. Saxl,*Linear groups with orders divisible by certain large primes*, (To Appear).

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Additional Information

**Shreeram S. Abhyankar**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Email:
ram@cs.purdue.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-96-03471-5

Received by editor(s):
March 21, 1995

Additional Notes:
This work was partly supported by NSF grant DMS 91–01424 and NSA grant MDA 904–92–H–3035.

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1996
American Mathematical Society