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The Erd{\\H o}s--Ginzburg--Ziv constant $\\mathsf s (G)$ of $G$ is defined as the smallest integer $l \\in \\mathbb N$ such that every sequence \\ $S$ \\ over $G$ of length $|S| \\ge l$ \\ has a zero-sum subsequence $T$ of length $|T| = \\exp (G)$. If $G$ has rank at most two, then the precise value of $\\mathsf s (G)$ is known (for cyclic groups this is the Theorem of Erd{\\H o}s-Ginzburg-Ziv). Only very little is known for groups of higher rank. 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 ","authors_text":"Qinghai Zhong, Weidong Gao, Yushuang Fan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2010-10-25T12:38:28Z","title":"On the Erd{\\H o}s--Ginzburg--Ziv constant of finite abelian groups of high rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5101","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ed61898b3c7f7535264344061d3dc0e4cb8a78db33bad0055a758958ba518673","target":"record","created_at":"2026-05-18T04:27:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8ad9e611e3b6974888ffc0f664138c5089ad71335db3d203d979fca7aa17549c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2010-10-25T12:38:28Z","title_canon_sha256":"e0ec0afdb46f9ef1768f6eb801c34525901e7553c59f2d5ebd803605a6138f5c"},"schema_version":"1.0","source":{"id":"1010.5101","kind":"arxiv","version":2}},"canonical_sha256":"0ca91ea72ddf602c5dc9b91ba3f2c5d3297fe27683801fc4f97985c540bdd428","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ca91ea72ddf602c5dc9b91ba3f2c5d3297fe27683801fc4f97985c540bdd428","first_computed_at":"2026-05-18T04:27:26.527539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:26.527539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eqWdAIJMZnZ6Rbjx85mcxuf7FRtEMdLr1nlbVaozCLOJuKvr7veDSE0h9Gc7Ci0zMDzUItiLZJvEL3BwAhadCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:26.527995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5101","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed61898b3c7f7535264344061d3dc0e4cb8a78db33bad0055a758958ba518673","sha256:9214552e8775ce36f0b6923be6e213d7bb4cb5f2c6718111053076f7dcc06fc0"],"state_sha256":"81e07ed8a897faff79d411da2cb494038fd200a4c9fefa4ed1512dd1e303dc1e"}