Rationality problem for some transitive subgroups of S₁₄

Abstract

Let G be a transitive subgroup of S₁₄. For any field k, let G act naturally on the rational function field $k(x_1,x_2,\dots ,x_{14})$ via k-automorphisms defined by $\sigma (x_i)=x_{\sigma (i)}$ for any $\sigma \in G$ and $1\le i\le 14.$ We will show the rationality of the fixed field $k{(x_1,x_2,\dots ,x_{14})}^G$ when G is an extension of an elementary abelian 2-group.

Keywords:

• Rationality problem
• transitive group
• Noether’s problem

2010 Mathematics Subject Classification:

• Primary: 12F20
• 13A50
• 14E08

Acknowledgment

The authors cordially thank the referees for their careful reading and helpful comments.

Additional information

Funding

This work was supported by National Natural Science Foundation of China (grant nos. 11871083, 11371044).