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
It is shown that no non-trivial composition of translations x x + a and odd rational powers x p/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)