{"paper":{"title":"Envelopes of certain solvable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Tullia Dymarz","submitted_at":"2014-04-21T03:22:04Z","abstract_excerpt":"A discrete subgroup $\\Gamma$ of a locally compact group $H$ is called a uniform lattice if the quotient $H/\\Gamma$ is compact. Such an $H$ is called an envelope of $\\Gamma$. In this paper we study the problem of classifying envelopes of various solvable groups including the solvable Baumslag-Solitar groups, lamplighter groups and certain abelian-by-cyclic groups. Our techniques are geometric and quasi-isometric in nature. In particular we show that for every $\\Gamma$ we consider there is a finite family of preferred model spaces $X$ such that, up to compact groups, $H$ is a cocompact subgroup "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5098","kind":"arxiv","version":1},"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"}