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Discrete subgroups of locally definable groups
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Authors
Advisor(s)
Abstract(s)
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
Description
Keywords
Covers Discrete subgroups Locally definable groups
Citation
Berarducci, A.; Edmundo, Mário Jorge; Mamino, M. - Discrete subgroups of locally definable groups. "Selecta Mathematica (New Series)" [Em linha]. ISSN 1420-9020 (Print) 1022-1824 (Online). Vol. 19, Nº 3 (2013), p. 1-17
Publisher
Springer-Verlag