Real Algebraic and Analytic Geometry |

Discrete Subgroups of Locally Definable Groups.

e-mail:

Submission: 2012, September 5.

*Abstract:
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.*

Mathematics Subject Classification (2010): 03C64, 03C68, 22B99.

Keywords and Phrases: Locally definable groups, covers, discrete subgroups.

**Full text**: http://arxiv.org/abs/1202.5649

Server Home Page