{"paper":{"title":"Construction of some subgroups in black box groups ${\\rm {PGL}}_2(q)$ and ${\\rm{(P)SL}}_2(q)$","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":"2014-03-10T12:18:59Z","abstract_excerpt":"For the black box groups $X$ encrypting ${\\rm{PGL}}_2(q)$, $q$ odd, we propose an algorithm constructing a subgroup encrypting ${\\rm{Sym}}_4$ and subfield subgroups of $X$. We also present the analogous algorithms for black box groups encrypting ${\\rm{(P)SL}}_2(q)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2224","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"}