Once more nice equations for nice groups

Authors:
Shreeram S. Abhyankar and Paul A. Loomis

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1885-1896

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

DOI:
https://doi.org/10.1090/S0002-9939-98-04421-9

MathSciNet review:
1459101

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In a previous paper, nice quintinomial equations were given for unramified coverings of the affine line in nonzero characteristic with the projective symplectic isometry group PSp and the (vectorial) symplectic isometry group Sp as Galois groups where is any integer and is any power of . Here we deform these equations to get nice quintinomial equations for unramified coverings of the once punctured affine line in characteristic with the projective symplectic similitude group PGSp and the (vectorial) symplectic similitude group GSp as Galois groups.

**[A01]**S. S. Abhyankar,*Local uniformization on algebraic surfaces over ground fields of characteristic*, Annals of Mathematics**63**(1956), 491-526. MR**17:1134d****[A02]**S. S. Abhyankar,*Coverings of algebraic curves*, American Journal of Mathematics**79**(1957), 825-856. MR**20:872****[A03]**S. S. Abhyankar,*Galois theory on the line in nonzero characteristic*, Bulletin of the American Mathematical Society**27**(1992), 68-133. MR**94a:12004****[A04]**S. S. Abhyankar,*Nice equations for nice groups*, Israel Journal of Mathematics**88**(1994), 1-24. MR**96f:12003****[A05]**S. S. Abhyankar,*Again nice equations for nice groups*, Proceedings of the American Mathematical Society**124**(1996), 2967-2976. MR**96m:12004****[A06]**S. S. Abhyankar,*More nice equations for nice groups*, Proceedings of the American Mathematical Society**124**(1996), 2977-2991. MR**96m:12005****[A07]**S. S. Abhyankar,*Further nice equations for nice groups*, Transactions of the American Mathematical Society**348**(1996), 1555-1577. MR**96m:14021****[A08]**S. S. Abhyankar,*Factorizations over finite fields*, Finite Fields and Applications, London Mathematical Society, Lecture Note Series**233**(1996), 1-21. CMP**97:08****[A09]**S. S. Abhyankar,*Projective polynomials*, Proceedings of the American Mathematical Society**125**(1997), 1643-1650. CMP**97:07****[BuS]**F. Buekenhout and E. E. Shult,*On the foundations of polar geometry*, Geometriae Dedicata**3**(1974), 155-170. MR**50:3091****[CaK]**P. J. Cameron and W. M. Kantor,*2-transitive and antiflag transitive collineation groups of finite projective spaces*, Journal of Algebra**60**(1979), 384-422. MR**81c:20032****[Kan]**W. M. Kantor,*Rank 3 characterizations of classical geometries*, Journal of Algebra**36**(1975), 309-313. MR**52:8229****[KLi]**P. Kleidman and M. W. Liebeck,*The Subgroup Structure of the Finite Classical Groups*, Cambridge University Press, Cambridge, 1990. MR**91g:20001****[Tit]**J. Tits,*Buildings of Spherical Type and Finite BN-Pairs*, Springer Lecture Notes In Mathematics Number 386, 1974. MR**57:9866****[Wae]**B. L. van der Waerden,*Modern Algebra, vol I*, Frederick Ungar Publishing Co., New York, 1949.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
12F10,
14H30,
20D06,
20E22

Retrieve articles in all journals with MSC (1991): 12F10, 14H30, 20D06, 20E22

Additional Information

**Shreeram S. Abhyankar**

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

Email:
ram@cs.purdue.edu

**Paul A. Loomis**

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

Email:
loomisp@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04421-9

Received by editor(s):
December 1, 1996

Additional Notes:
The first author’s work was partly supported by NSA grant MDA 904-97-1-0010, and the second author’s work was partly supported by a PRF grant at Purdue University.

Communicated by:
Ronald M. Solomon

Article copyright:
© Copyright 1998
American Mathematical Society