Rationality problem for transitive subgroups of S_8

Abstract

For any field K and any transitive subgroup G of S_8, let G acts naturally on K(x_1, . . ., x_8) by permutations of the variables, we prove that under some minor conditions K(x_1, . . ., x_8)^G is always K-rational except G is A_8 or G is isomorphic to PGL(2, 7). We pay special attentions on the characteristic 2 cases.

arXiv comment29 pages

References in corpus (1)

• Rational invariants for subgroups of S_5 and S_7

Cited by in corpus (1)

• Noether's problem for some subgroups of $S_{14}$: the modular case