{"paper":{"title":"Free subgroups of special linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Rupert McCallum","submitted_at":"2014-03-31T15:47:20Z","abstract_excerpt":"We present a proof of the following claim. Suppose that $n$ is an integer such that $n>1$ and that $k$ is any field. Suppose that $g$ is an element of $\\mathrm{SL}(n,k)$ of infinite order. Then the set $\\{h\\in\\mathrm{SL}(n,k)\\mid <g,h>$ is a free group of rank two$\\}$ is a Zariski dense subset of $\\mathrm{SL}(n,\\bar{k})$ where $\\bar{k}$ is an algebraic closure of $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.8060","kind":"arxiv","version":6},"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"}