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Composites of translations and odd rational powers act freely

Published online by Cambridge University Press:  17 April 2009

Stephen D. Cohen  and
A.M.W. Glass
Stephen D. Cohen
Affiliation:
Department of MathematicsUniversity of GlasgowGlasgow G12 8QW, Scotland
A.M.W. Glass
Affiliation:
Department of Mathematics and StatisticsBowling Green State UniversityBowling Green OH 43403-0221, United States of America
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 1 , February 1995 , pp. 73 - 81
Copyright
Copyright © Australian Mathematical Society 1995

References

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