Compact-like abelian groups without non-trivial quasi-convex null sequences

0. We characterize groups with this property in the following classes of groups: (a) bounded precompact abelian groups; (b) minimal abelian groups; (c) totally minimal abelian groups; (d) \omega-bounded abelian groups. We also provide examples of minimal abelian groups with this property, and show that there exists a minimal pseudocompact abelian group with the same property; furthermore, under Martin's Axiom, the group may be chosen to be countably compact minimal abelian.
Comment: Final version -->
Druh dokumentu: Working Paper
DOI: 10.1016/j.jpaa.2013.05.001
Přístupová URL adresa: http://arxiv.org/abs/1007.1927
Přírůstkové číslo: edsarx.1007.1927
Autor: Dikranjan, D., Lukács, Gábor
Rok vydání: 2010
Předmět:
Zdroj: J. Pure Appl. Algebra 218 (2014), 135-147
Druh dokumentu: Working Paper
DOI: 10.1016/j.jpaa.2013.05.001
Popis: In this paper, we study precompact abelian groups G that contain no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0. We characterize groups with this property in the following classes of groups: (a) bounded precompact abelian groups; (b) minimal abelian groups; (c) totally minimal abelian groups; (d) \omega-bounded abelian groups. We also provide examples of minimal abelian groups with this property, and show that there exists a minimal pseudocompact abelian group with the same property; furthermore, under Martin's Axiom, the group may be chosen to be countably compact minimal abelian.
Comment: Final version
Databáze: arXiv
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