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Original Paper
A remark on divisibility of definable groups
Article first published online: 28 SEP 2005
DOI: 10.1002/malq.200510014
Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1521-3870/asset/cover.gif?v=1&s=3df32dbed8d9153ac6eafe1eaa786854b9b48345 "Mathematical Logic Quarterly")
Additional Information
How to Cite
Edmundo, M. J. (2005), A remark on divisibility of definable groups. Mathematical Logic Quarterly, 51: 639–641. doi: 10.1002/malq.200510014
Publication History
- Issue published online: 28 SEP 2005
- Article first published online: 28 SEP 2005
- Manuscript Revised: 5 SEP 2005
- Manuscript Accepted: 5 SEP 2005
- Manuscript Received: 29 JUN 2005
- Abstract
- References
- Cited By
Keywords:
- O-minimal structures;
- definable groups
Abstract
We show that if G is a definably compact, definably connected definable group defined in an arbitrary o-minimal structure, then G is divisible. Furthermore, if G is defined in an o-minimal expansion of a field, k ∈ ℕ and pk : G → G is the definable map given by pk (x ) = xk for all x ∈ G , then we have |(pk )–1(x )| ≥ kr for all x ∈ G , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)