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A remark on divisibility of definable groups

✍ Scribed by Mário J. Edmundo

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
89 KB
Volume
51
Category
Article
ISSN
0044-3050

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✦ Synopsis

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 p k : G -→ G is the definable map given by p k (x) = x k for all x ∈ G, then we have |(p k ) -1 (x)| ≥ k r for all x ∈ G, where r > 0 is the maximal dimension of abelian definable subgroups of G.

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