有理性问题的一点注记

A Note on Rationality Problem

摘要: 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,···,x₄)上的作用定义为σ(x_i)=x_σ(i)，对任意的σ∈G，1≤i≤14 。我们将证明k(G)=k(x₁,x₂,···,x₄)^G是k-有理的。

Abstract: 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(x_i)=x_σ(i), for any σ∈G, any 1≤i≤14. We will show k(G)=k(x₁,x₂,···,x₄)^G is k-rational.