Bulletin of the Australian Mathematical Society

Table of Contents - 1995 - Volume 51, Issue 01  

Research Article

Composites of translations and odd rational powers act freely

Stephen D. Cohena1 and A.M.W. Glassa2

a1 Department of Mathematics University of Glasgow Glasgow G12 8QW, Scotland

a2 Department of Mathematics and Statistics Bowling Green State University Bowling Green OH 43403-0221, United States of America

Abstract

It is shown that no non-trivial composition of translations x xs21A6 x + a and odd rational powers x xs21A6p/q, where p,q are odd co-prime integers, positive or negative with p/q≠±, acts like the identity on a field of characteristic zero. This extends a theorem of Adeleke, Glass, and Morley in which only odd positive rational powers were considered. Moreover, the nature of the proof itself (by field theory) is a simplification and natural refinement of previous proofs. It has applications in other settings.

(Received March 17 1994)