有理性问题的一点注记

A Note on Rationality Problem

设群G为S14的传递子群,其为两个群的圈积。令k为任意域,G在有理函数域k(x1,x2,…x14)上的作用定义为σ(xi)=xσ(i),对任意的σ∈G,1≤i≤14 。我们将证明k(G)=k(x1,x2,…x14)G是k-有理的。

Let G be a transitive subgroup of S14 which is a wreath product. For any field k, G acts on the rational function field k(x1,x2,···,x4) via k-automorphisms defined by σ(xi)=xσ(i), for any σ∈G, any 1≤i≤14. We will show k(G)=k(x1,x2,···,x4)G is k-rational.