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If |G| > 1, then D (G) <= t (H) <= 1 + D (G) (D (G) -1) / 2, where D (G) is the Davenport constant of G. We analyze the case when t (H) equals the lower bound, and we show that t (H) grows asymptotically as the upper bound, when both terms are considered as functions of the rank of G. We provide more precise results if G is either cyclic or an elementary 2-group."},"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":"1302.3078","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-02-13T13:26:54Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0a1b94ba3b635c9301f8a89fa45b4b224311c5e79038dca297e144af900bc7a7","abstract_canon_sha256":"ec4c1ae30f573fbfc53436dc5728f2a04816948d7c588f4d86ef84d61b41bb0c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:35.176096Z","signature_b64":"qTVxUTkk5h9s4EJ/JNesNKznSYO0JS2SO2qAKoEfOZXJBcT2dCqn/zkPPfkuVV40HQcqXAcUvCioaCr1mLnrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b23a850bdc1f02f47e793b9ef34646cecfafa38c48c3d6a6d4800b98e982c889","last_reissued_at":"2026-05-18T03:20:35.175114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:35.175114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local and global tameness in Krull monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Alfred Geroldinger (IM), W. 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