{"paper":{"title":"Compact-like abelian groups without non-trivial quasi-convex null sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"D. Dikranjan, G\\'abor Luk\\'acs","submitted_at":"2010-07-12T15:42:50Z","abstract_excerpt":"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:\n  (a) bounded precompact abelian groups;\n  (b) minimal abelian groups;\n  (c) totally minimal abelian groups;\n  (d) \\omega-bounded abelian groups.\n  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 gro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1927","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}