{"paper":{"title":"Correction of a theorem on the symmetric group generated by transvections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Hau-wen Huang","submitted_at":"2011-08-03T03:59:05Z","abstract_excerpt":"Let $V$ denote a vector space over two-element field $\\mathbb F_2$ with finite positive dimension and endowed with a symplectic form $B.$ Let ${\\rm SL}(V)$ denote the special linear group of $V.$ Let $S$ denote a subset of $V.$ Define $Tv(S)$ as the subgroup of ${\\rm SL}(V)$ generated by the transvections with direction $\\alpha$ for all $\\alpha\\in S.$ Define $G(S)$ as the graph whose vertex set is $S$ and where $\\alpha,\\beta\\in S$ are connected whenever $B(\\alpha,\\beta)=1.$ A well-known theorem states that under the assumption that $S$ spans $V,$ the following (i), (ii) are equivalent:\n(i) $Tv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2409","kind":"arxiv","version":2},"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"}