{"paper":{"title":"Adjoint representations of black box groups ${\\rm PSL}_2(\\mathbb{F}_q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexandre Borovik, \\c{S}\\\"ukr\\\"u Yal\\c{c}{\\i}nkaya","submitted_at":"2015-02-23T10:26:22Z","abstract_excerpt":"Given a black box group $\\mathsf{Y}$ encrypting $\\rm{PSL}_2(\\mathbb{F})$ over an unknown field $\\mathbb{F}$ of unknown odd characteristic $p$ and a global exponent $E$ for $\\mathsf{Y}$ (that is, an integer $E$ such that $\\mathsf{y}^E=1$ for all $\\mathsf{y} \\in \\mathsf{Y}$), we present a Las Vegas algorithm which constructs a unipotent element in $\\mathsf{Y}$. The running time of our algorithm is polynomial in $\\log E$. This answers the question posed by Babai and Beals in 1999. We also find the characteristic of the underlying field in time polynomial in $\\log E$ and linear in $p$.\n  Furthermo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06374","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"}