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In the present paper, we focus on groups of the form $G = C_n^r$, with $n, r \\in \\N$ and $n \\ge 2$, and we tackle the study "},"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":"1010.5101","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2010-10-25T12:38:28Z","cross_cats_sorted":[],"title_canon_sha256":"e0ec0afdb46f9ef1768f6eb801c34525901e7553c59f2d5ebd803605a6138f5c","abstract_canon_sha256":"8ad9e611e3b6974888ffc0f664138c5089ad71335db3d203d979fca7aa17549c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:26.527995Z","signature_b64":"eqWdAIJMZnZ6Rbjx85mcxuf7FRtEMdLr1nlbVaozCLOJuKvr7veDSE0h9Gc7Ci0zMDzUItiLZJvEL3BwAhadCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ca91ea72ddf602c5dc9b91ba3f2c5d3297fe27683801fc4f97985c540bdd428","last_reissued_at":"2026-05-18T04:27:26.527539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:26.527539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Erd{\\H o}s--Ginzburg--Ziv constant of finite abelian groups of high rank","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qinghai Zhong, Weidong Gao, Yushuang Fan","submitted_at":"2010-10-25T12:38:28Z","abstract_excerpt":"Let $G$ be a finite abelian group. 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