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Definable quotients of locally definable groups

✍ Scribed by Pantelis E. Eleftheriou, Ya’acov Peterzil

Book ID: 118777650
Publisher: SP Birkhäuser Verlag Basel
Year: 2012
Tongue: English
Weight: 289 KB
Volume: 18
Category: Article
ISSN: 1022-1824
DOI: 10.1007/s00029-012-0091-5

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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