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Let $D_{2n}$ be the Dihedral Group of order $2n$ and $Q_{4n}$ be the Dicyclic Group of order $4n$. J. J. Zhuang and W. Gao (European J. Combin. 26 (2005), 1053-1059) showed that $D(D_{2n}) = n+1$ and J. Bass (J. Number Theory 126 (2007), 217-236) showed that $D(Q_{4n}) = 2n+1$. In this paper, we give explicit characterizations of all sequences $S$ of $G$ such that $|S| = D(G)"},"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":"1701.08788","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-30T19:21:47Z","cross_cats_sorted":[],"title_canon_sha256":"9a76d7715354799ab2e845a3f738197684607049282313e15f191c17e24527c4","abstract_canon_sha256":"7078cdfae90971d3ab9ebbe04d2425e948e1900bfdcd665a16ebbd80b4cf5cd0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:39.181422Z","signature_b64":"82MUvfAl7hu8EMmnHLNcoVD3VGfK0lNZx5OWz4DcPy+yoaSwas5Ta4j8bGV4ZeaYNBfxcZ6iPtWLH0ooI20VBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"226875e6994f18956881a8351d7746f6bc8789d751b7a8a4586ad212a1e73506","last_reissued_at":"2026-05-18T00:51:39.181018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:39.181018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal product-one free sequences in Dihedral and Dicyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabio Enrique Brochero Mart\\'inez, S\\'avio Ribas","submitted_at":"2017-01-30T19:21:47Z","abstract_excerpt":"Let $G$ be a finite group, written multiplicatively. The Davenport constant of $G$ is the smallest positive integer $D(G)$ such that every sequence of $G$ with $D(G)$ elements has a non-empty subsequence with product $1$. Let $D_{2n}$ be the Dihedral Group of order $2n$ and $Q_{4n}$ be the Dicyclic Group of order $4n$. J. J. Zhuang and W. Gao (European J. Combin. 26 (2005), 1053-1059) showed that $D(D_{2n}) = n+1$ and J. Bass (J. Number Theory 126 (2007), 217-236) showed that $D(Q_{4n}) = 2n+1$. 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