{"paper":{"title":"Subnormal closure of a homomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Emmanuel D. Farjoun, Yoav Segev","submitted_at":"2014-05-01T04:24:03Z","abstract_excerpt":"Let $\\varphi\\colon\\Gamma\\to G$ be a homomorphism of groups. In this paper we introduce the notion of a subnormal map (the inclusion of a subnormal subgroup into a group being a basic prototype). We then consider factorizations $\\Gamma\\xrightarrow{\\psi} M\\xrightarrow{n} G$ of $\\varphi,$ with $n$ a subnormal map. We search for a universal such factorization. When $\\Gamma$ and $G$ are finite we show that such universal factorization exists: $\\Gamma\\to\\Gamma_{\\infty}\\to G,$ where $\\Gamma_{\\infty}$ is a hypercentral extension of the subnormal closure $\\mathcal{C}$ of $\\varphi(\\Gamma)$ in $G$ (i.e.~"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0090","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"}