Further Nice Equations for Nice Groups

Abhyankar, Shreeram

doi:10.1090/S0002-9947-96-01584-X

Further Nice Equations for Nice Groups
HTML articles powered by AMS MathViewer

by Shreeram S. Abhyankar PDF

Trans. Amer. Math. Soc. 348 (1996), 1555-1577 Request permission

Abstract:

Nice sextinomial equations are given for unramified coverings of the affine line in nonzero characteristic $p$ with P$\Omega ^{-}(2m,q)$ and $\Omega ^{-}(2m,q)$ as Galois groups where $m>3$ is any integer and $q>1$ is any power of $p>2$.

References

Shreeram Abhyankar, Coverings of algebraic curves, Amer. J. Math. 79 (1957), 825–856. MR 94354, DOI 10.2307/2372438
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 104675, DOI 10.2307/2372850
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
L. Kantorovitch, The method of successive approximations for functional equations, Acta Math. 71 (1939), 63–97. MR 95, DOI 10.1007/BF02547750
S. S. Abhyankar, More nice equations for nice groups, Proceedings of the American Mathematical Society (to appear).
Michael Aschbacher, Finite group theory, Cambridge Studies in Advanced Mathematics, vol. 10, Cambridge University Press, Cambridge, 1986. MR 895134
Francis Buekenhout and Ernest Shult, On the foundations of polar geometry, Geometriae Dedicata 3 (1974), 155–170. MR 350599, DOI 10.1007/BF00183207
P. J. Cameron and W. M. Kantor, $2$-transitive and antiflag transitive collineation groups of finite projective spaces, J. Algebra 60 (1979), no. 2, 384–422. MR 549937, DOI 10.1016/0021-8693(79)90090-5
L. E. Dickson, Linear Groups, Teubner, 1901.
William M. Kantor, Rank $3$ characterizations of classical geometries, J. Algebra 36 (1975), no. 2, 309–313. MR 387386, DOI 10.1016/0021-8693(75)90106-4
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, DOI 10.1017/CBO9780511629235
Donald E. Taylor, The geometry of the classical groups, Sigma Series in Pure Mathematics, vol. 9, Heldermann Verlag, Berlin, 1992. MR 1189139
Jacques Tits, Buildings of spherical type and finite BN-pairs, Lecture Notes in Mathematics, Vol. 386, Springer-Verlag, Berlin-New York, 1974. MR 0470099