{"paper":{"title":"Pathological and Omega-transitive Representations of Free Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Jorge Bruno","submitted_at":"2012-04-25T11:01:49Z","abstract_excerpt":"Given a linear order $\\Omega$ its automorphism group $\\Aut(\\Omega)$ forms a lattice-ordered group via pointwise order. Assuming the continuum to be a regular cardinal, we show that \\emph{pathological} and \\emph{$\\omega$-transitive} (i.e. highly transitive) representations of free groups abound within \\emph{large} permutation groups of linear orders. Consequently, under the Generalized Continuum Hypothesis it is then true that given any linear order $\\Omega$ for which $|\\Omega| = $ cof$(\\Omega) = \\aleph_i$ ($i \\in \\N$) then any permutation group that is large in $\\Aut(\\Omega)$ contains an $\\ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5615","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"}