{"paper":{"title":"Maximal subsemigroups of the semigroup of all mappings on an infinite set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"J. D. Mitchell, J. East, Y. P\\'eresse","submitted_at":"2011-04-11T17:27:24Z","abstract_excerpt":"In this paper we classify the maximal subsemigroups of the \\emph{full transformation semigroup} $\\Omega^\\Omega$, which consists of all mappings on the infinite set $\\Omega$, containing certain subgroups of the symmetric group $\\sym(\\Omega)$ on $\\Omega$. In 1965 Gavrilov showed that there are five maximal subsemigroups of $\\Omega^\\Omega$ containing $\\sym(\\Omega)$ when $\\Omega$ is countable and in 2005 Pinsker extended Gavrilov's result to sets of arbitrary cardinality.\n  We classify the maximal subsemigroups of $\\Omega^\\Omega$ on a set $\\Omega$ of arbitrary infinite cardinality containing one o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2011","kind":"arxiv","version":4},"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"}