H. W. Lenstra, Jr., M. Zieve, A family of exceptional polynomials in characteristic three, in S. Cohen, H. Niederreiter, eds., Finite Fields and Applications, vol. 233 of Lecture Note Series, Cambridge (1996), Cambridge University Press, 1996 pp. 209--218.  Home/Search   Document Details and Download   Summary   Related Articles

....the action on the roots of f(X) Gamma t, this follows from proof of Theorem 2.10. 12 In [FGS93] the possible monodromy groups of exceptional polynomials have been classified, and the question about existence of actual examples has been answered positively for all non affine groups in [CM94] LZ96] and for some affine groups in [GM97] There is little hope to achieve an analogous result for rational functions rather than polynomials. The reason is that in positive characteristic, the condition that K(X)jK(f(X) is an extension of genus 0 fields gives little constraints on the group G. ....

....We first assume that L = L 2 (p a ) with p prime and p a 3. The examples include the important examples discovered in [FGS93] with p = 2 or 3, a 1 odd, A = Aut(L) and M the normalizer of a nonsplit torus. These lead to interesting families of exceptional polynomials (see [Mul94] CM94] LZ96] GZ] Theorem 3.27. Let G = L 2 (2 a ) with a 1 odd. Let H be a proper subgroup of G. The following are equivalent: i) There exist subgroups M and A of Aut(G) with G A such that A = GM and G M = H with (A; G; A=M) exceptional; ii) L 2 (2) H and (3; G : H] 1; iii) H ....

H. W. Lenstra, Jr., M. Zieve, A family of exceptional polynomials in characteristic three, in S. Cohen, H. Niederreiter, eds., Finite Fields and Applications, vol. 233 of Lecture Note Series, Cambridge (1996), Cambridge University Press, 1996 pp. 209--218.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC