Nonrational fixed fields

James K. Deveney and Joe Yanik

Vol. 139 (1989), No. 1, 45–51

DOI: 10.2140/pjm.1989.139.45

Abstract

We present an example of a flag of rational extensions, stabilized by the action of the group of order 2 such that the fixed field under the group action is not retract rational and hence not rational. This fixed field is shown to be a genus 0 extension of a pure transcendental extension.

Mathematical Subject Classification 2000

Primary: 12F20

Milestones

Received: 4 September 1987

Revised: 25 May 1988

Published: 1 September 1989