{"paper":{"title":"All januarials constructed from Hecke groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Qaiser Mushtaq, Saadia Mehwish","submitted_at":"2018-09-29T12:48:33Z","abstract_excerpt":"Professor Graham Higman defined januarial as a special instance of map constructed from embedding of a coset diagram for an action of $\\Delta (2,\\ell ,k)$, on finite sets yielding exactly two orbits of the product of the two generators, having equal sizes. In this paper we determine a condition for the existence of a januarial from $\\Delta (2,\\ell ,k),$ the quotients of Hecke groups $H_{\\Lambda _{\\ell }},$ when acting on the projective lines over finite fields $PL(F_{q})$. We develope a method to find all the januarials from Hecke groups $H_{\\Lambda _{\\ell }}$, when the triangle group $\\Delta "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00203","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"}