{"paper":{"title":"Beauville $p$-groups of wild type and groups of maximal class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Carlo M. Scoppola, \\c{S}\\\"ukran G\\\"ul, Gustavo A. Fern\\'andez-Alcober, Norberto Gavioli","submitted_at":"2017-01-25T15:55:13Z","abstract_excerpt":"Let $G$ be a Beauville finite $p$-group. If $G$ exhibits a `good behaviour' with respect to taking powers, then every lift of a Beauville structure of $G/\\Phi(G)$ is a Beauville structure of $G$. We say that $G$ is a Beauville $p$-group of wild type if this lifting property fails to hold. Our goal in this paper is twofold: firstly, we fully determine the Beauville groups within two large families of $p$-groups of maximal class, namely metabelian groups and groups with a maximal subgroup of class at most $2$; secondly, as a consequence of the previous result, we obtain infinitely many Beauville"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07361","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"}