{"paper":{"title":"Doubly Hurwitz Beauville groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.GR","authors_text":"Emilio Pierro, Gareth A. Jones","submitted_at":"2017-09-27T10:42:15Z","abstract_excerpt":"If $\\mathcal S$ is a Beauville surface $({\\mathcal C}_1\\times{\\mathcal C}_2)/G$, then the Hurwitz bound implies that $|G|\\le 1764\\,\\chi({\\mathcal S})$, with equality if and only if the Beauville group $G$ acts as a Hurwitz group on both curves ${\\mathcal C}_i$. Equivalently, $G$ has two generating triples of type $(2,3,7)$, such that no generator in one triple is conjugate to a power of a generator in the other. We show that this property is satisfied by alternating groups $A_n$, their double covers $2.A_n$, and special linear groups $SL_n(q)$ if $n$ is sufficiently large, but by no sporadic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09441","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"}