The rationality problem for purely monomial group actions

Abstract

We investigate the rationality problem for purely monomial actions of finite groups. We solve it affirmatively in the following case: K is a field with char K ≠ 2 and G is a subgroup of GL(n; ℤ) isomorphic to (C 2 ), where n > 0. Then the fixed field of K(x 1, ... x n ) under the purely monomial action of G is rational over K.