Noether's problem for y Ŝ4 and y Ŝ5
Journal
Pacific Journal of Mathematics
Journal Volume
258
Journal Issue
2
Pages
349-368
Date Issued
2012
Author(s)
Abstract
Let k be a field, let G be a finite group and let k.x g W g 2 G / be the rational function field over k, on which G acts by the k-automorphisms defined by h x g D x hg for any g; h 2 G .Noether's problem asks whether the fixedS n is the double cover of the symmetric group S n , in which the liftings of transpositions and products of disjoint transpositions are of order 4, Serre shows that .ޑ b S 4 / and .ޑ b S 5 / are not -ޑrational.We will prove that if k is a field such that char k ¤ 2 ; 3, and k. 8 / is a cyclic extension of k, then k. b
Type
journal article