A remark on divisibility of definable groups

Edmundo, Mário Jorge

http://hdl.handle.net/10400.2/2842

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Authors

Edmundo, Mário Jorge

Abstract(s)

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.

Keywords

Definable groups O-minimal structures

URI

http://hdl.handle.net/10400.2/2842

Citation

Edmundo, Mário Jorge - A remark on divisibility of definable groups. "Mathematical Logic Quarterly" [Em linha]. ISSN 0942-5616 (Print) 1521-3870 (Online).Vol. 51, Nº 6 (2005), p. 1-7