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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.07361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-01-25T15:55:13Z","cross_cats_sorted":[],"title_canon_sha256":"aa9d879e211622a999ceebec8cb14a742eb9bee246dc6448728b8af7ae20e0b7","abstract_canon_sha256":"86a2081a4feee69782840f6b0b3cd0076a79dee6d8b288e559af4ac5b6dfc1e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:04.762975Z","signature_b64":"lkZOgBYeyCWwR+2OmMdfK/nLeuh/OJ9nRPoSRba9XoG8bFPQZb4hTT2NzdCd1ogRq90k5hNrOkFO7CTlCTfjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e44a255b102e7c06c5ddc8d8a3a5b8fe126d659e4b17e41ab8b0b07418853cc4","last_reissued_at":"2026-05-18T00:52:04.762438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:04.762438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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