Once more nice equations for nice groups
Authors:
Shreeram S. Abhyankar and Paul A. Loomis
Journal:
Proc. Amer. Math. Soc. 126 (1998), 18851896
MSC (1991):
Primary 12F10, 14H30, 20D06, 20E22
MathSciNet review:
1459101
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Abstract 
References 
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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]
Shreeram
Abhyankar, Local uniformization on algebraic surfaces over ground
fields of characteristic 𝑝≠0, Ann. of Math. (2)
63 (1956), 491–526. MR 0078017
(17,1134d)
 [A02]
Shreeram
Abhyankar, Coverings of algebraic curves, Amer. J. Math.
79 (1957), 825–856. MR 0094354
(20 #872)
 [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
(94a:12004), http://dx.doi.org/10.1090/S027309791992002707
 [A04]
Shreeram
S. Abhyankar, Nice equations for nice groups, Israel J. Math.
88 (1994), no. 13, 1–23. MR 1303488
(96f:12003), http://dx.doi.org/10.1007/BF02937504
 [A05]
Shreeram
S. Abhyankar, Again nice equations for nice
groups, Proc. Amer. Math. Soc.
124 (1996), no. 10, 2967–2976. MR 1343675
(96m:12004), http://dx.doi.org/10.1090/S0002993996034715
 [A06]
Shreeram
S. Abhyankar, More nice equations for nice
groups, Proc. Amer. Math. Soc.
124 (1996), no. 10, 2977–2991. MR 1343676
(96m:12005), http://dx.doi.org/10.1090/S0002993996034727
 [A07]
Shreeram
S. Abhyankar, Further nice equations for nice
groups, Trans. Amer. Math. Soc.
348 (1996), no. 4,
1555–1577. MR 1348146
(96m:14021), http://dx.doi.org/10.1090/S000299479601584X
 [A08]
S. S. Abhyankar, Factorizations over finite fields, Finite Fields and Applications, London Mathematical Society, Lecture Note Series 233 (1996), 121. CMP 97:08
 [A09]
S. S. Abhyankar, Projective polynomials, Proceedings of the American Mathematical Society 125 (1997), 16431650. CMP 97:07
 [BuS]
Francis
Buekenhout and Ernest
Shult, On the foundations of polar geometry, Geometriae
Dedicata 3 (1974), 155–170. MR 0350599
(50 #3091)
 [CaK]
P.
J. Cameron and W.
M. Kantor, 2transitive and antiflag transitive collineation groups
of finite projective spaces, J. Algebra 60 (1979),
no. 2, 384–422. MR 549937
(81c:20032), http://dx.doi.org/10.1016/00218693(79)900905
 [Kan]
William
M. Kantor, Rank 3 characterizations of classical geometries,
J. Algebra 36 (1975), no. 2, 309–313. MR 0387386
(52 #8229)
 [KLi]
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
(91g:20001)
 [Tit]
Jacques
Tits, Buildings of spherical type and finite BNpairs, Lecture
Notes in Mathematics, Vol. 386, SpringerVerlag, Berlin, 1974. MR 0470099
(57 #9866)
 [Wae]
B. L. van der Waerden, Modern Algebra, vol I, Frederick Ungar Publishing Co., New York, 1949.
 [A01]
 S. S. Abhyankar, Local uniformization on algebraic surfaces over ground fields of characteristic , Annals of Mathematics 63 (1956), 491526. MR 17:1134d
 [A02]
 S. S. Abhyankar, Coverings of algebraic curves, American Journal of Mathematics 79 (1957), 825856. MR 20:872
 [A03]
 S. S. Abhyankar, Galois theory on the line in nonzero characteristic, Bulletin of the American Mathematical Society 27 (1992), 68133. MR 94a:12004
 [A04]
 S. S. Abhyankar, Nice equations for nice groups, Israel Journal of Mathematics 88 (1994), 124. MR 96f:12003
 [A05]
 S. S. Abhyankar, Again nice equations for nice groups, Proceedings of the American Mathematical Society 124 (1996), 29672976. MR 96m:12004
 [A06]
 S. S. Abhyankar, More nice equations for nice groups, Proceedings of the American Mathematical Society 124 (1996), 29772991. MR 96m:12005
 [A07]
 S. S. Abhyankar, Further nice equations for nice groups, Transactions of the American Mathematical Society 348 (1996), 15551577. MR 96m:14021
 [A08]
 S. S. Abhyankar, Factorizations over finite fields, Finite Fields and Applications, London Mathematical Society, Lecture Note Series 233 (1996), 121. CMP 97:08
 [A09]
 S. S. Abhyankar, Projective polynomials, Proceedings of the American Mathematical Society 125 (1997), 16431650. CMP 97:07
 [BuS]
 F. Buekenhout and E. E. Shult, On the foundations of polar geometry, Geometriae Dedicata 3 (1974), 155170. MR 50:3091
 [CaK]
 P. J. Cameron and W. M. Kantor, 2transitive and antiflag transitive collineation groups of finite projective spaces, Journal of Algebra 60 (1979), 384422. MR 81c:20032
 [Kan]
 W. M. Kantor, Rank 3 characterizations of classical geometries, Journal of Algebra 36 (1975), 309313. 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 BNPairs, 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.
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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:
http://dx.doi.org/10.1090/S0002993998044219
PII:
S 00029939(98)044219
Received by editor(s):
December 1, 1996
Additional Notes:
The first author’s work was partly supported by NSA grant MDA 9049710010, 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
