Once more nice equations for nice groups. (English) Zbl 0889.12005
Summary: In a previous paper [S. S. Abhyankar, Proc. Am. Math. Soc. 124, 2977-2991 (1996; Zbl 0866.12005)] nice quintinomial equations were given for unramified coverings of the affine line in nonzero characteristic \(p\) with the projective symplectic isometry group \(\text{PSp} (2m,q)\) and the (vectorial) symplectic isometry group \(\text{Sp} (2m,q)\) as Galois groups, where \(m>2\) is any integer and \(q>1\) is any power of \(p\). Here we deform these equations to get nice quintinomial equations for unramified coverings of the once punctured affine line in characteristic \(p\) with the projective symplectic similitude group \(\text{PGSp} (2m,q)\) and the (vectorial) symplectic similitude group \(\text{GSp} (2m,q)\) as Galois groups.
MSC:
12F10 | Separable extensions, Galois theory |
14H30 | Coverings of curves, fundamental group |
20D06 | Simple groups: alternating groups and groups of Lie type |
20E22 | Extensions, wreath products, and other compositions of groups |