{"paper":{"title":"Dense free subgroups of automorphism groups of homogeneous partially ordered sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Filip Strobin, Przemys{\\l}aw Gordinowicz, Szymon G{\\l}\\k{a}b","submitted_at":"2017-08-02T13:54:09Z","abstract_excerpt":"A countable poset is ultrahomogeneous if every isomorphism between its finite subposets can be extended to an automorphism. The groups $\\operatorname{Aut}(A)$ of such posets $A$ have a natural topology in which $\\operatorname{Aut}(A)$ are Polish topological groups. We consider the problem whether $\\operatorname{Aut}(A)$ contains a dense free subgroup of two generators. We show that if $A$ is ultrahomogeneous, then $\\operatorname{Aut}(A)$ contains such subgroup. Moreover, we characterize whose countable ultrahomogeneous posets $A$ such that for each natural $m$, the set of all cyclically dense "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00746","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"}