Composites of translations and odd rational powers act freely

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...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 1995-02, Vol.51 (1), p.73-81
Main Authors: Cohen, Stephen D., Glass, A.M.W.
Format: Article
Language:English
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Summary: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.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700013903