Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.2/2762
Título: Discrete subgroups of locally definable groups
Autor: Berarducci, A.
Edmundo, Mário Jorge
Mamino, M.
Palavras-chave: Covers
Discrete subgroups
Locally definable groups
Data: Ago-2013
Editora: Springer-Verlag
Citação: 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
Resumo: 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
Peer review: yes
URI: http://hdl.handle.net/10400.2/2762
ISSN: 1022-1824
1420-9020
Versão do Editor: http://link.springer.com/article/10.1007%2Fs00029-013-0123-9
Aparece nas colecções:Matemática e Estatística - Artigos em revistas internacionais / Papers in international journals

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