{"paper":{"title":"Semigroup Conjectures for Central Semidirect Product of R^n with R^m","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Kevin Lui, Siddharth Venkatesh, Viorel Nitica","submitted_at":"2013-09-30T11:33:36Z","abstract_excerpt":"In this paper we prove two new results about closed semigroups in the family of solvable groups H_{mn} that are semidirect products of R^m and R^n, and for which the structure homomorphism maps nontrivially into the center of Aut(R^n). The first result states that the closure of a semigroup generated by a set in H_{mn} that is not included in a maximal semigroup with nonempty interior is actually a group. The second result states that among the subsets of H_{mn} that are not included in a maximal proper semigroup, those that generate H_{mn} as a closed semigroup are dense. Results of this natu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7800","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"}