Rational invariants for subgroups of S5 and S7
Journal
Journal of Algebra
Journal Volume
413
Pages
345-363
Date Issued
2014
Author(s)
Abstract
Let G be a subgroup of S n, the symmetric group of degree n. For any field k, G acts naturally on the rational function field k(x1, x2, . . . , x n) via k-automorphisms defined by σ · x i = xσ(i) for any σ ∈ G, any 1 ≤ i ≤ n. TheoremIf n ≤ 5, then the fixed field k(x1,. . .,xn)G is purely transcendental over k. We will show that C(x1,. . .,x7)G is also purely transcendental over C if G is any transitive subgroups of S7 other than A7; a similar result is valid for solvable transitive subgroups of S11. © 2014.
Type
journal article