Rationality for subgroups of S_6

Abstract

For a transitive subgroup $G\le S_6$ which contain $C_3\times C_3$ as subgroup, we prove that $K(x_1,\dots ,x_6{)}^G$ is rational over $K$, where $K$ is any field, and $G$ acts naturally on $K(x_1,\dots ,x_6)$ by permutations on the variables. We also give an application on construction of generic polynomials.

arXiv comment10 pages