We work in the category of locally definable groups in an o-minimal expansion of a field. Eleftheriou and Peterzil conjectured that every definably generated abelian connected group G in this category is a cover of a definable group. We prove that this is the case under a natural convexity assumption inspired by the same authors, which in fact gives a necessary and sufficient condition. The proof is based on the study of the zero-dimensional compatible subgroups of G. Given a locally definable connected group G (not necessarily definably generated), we prove that the n-torsion subgroup of G is finite and that every zero-dimensional compatible subgroup of G has finite rank. Under a convexity hypothesis we show that every zero-dimensional compatible subgroup of G is finitely generated.
|Autori:||Berarducci A; Mario Edmundo; Marcello Mamino|
|Titolo:||Discrete subgroups of locally definable groups|
|Anno del prodotto:||2013|
|Digital Object Identifier (DOI):||10.1007/s00029-013-0123-9|
|Appare nelle tipologie:||1.1 Articolo in rivista|