{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RAHMUITUEBU2FBGP6P6GFFLTXA","short_pith_number":"pith:RAHMUITU","schema_version":"1.0","canonical_sha256":"880eca22742069a284cff3fc629573b81a0e33014a511af44d328b57d2e405a9","source":{"kind":"arxiv","id":"1112.1671","version":2},"attestation_state":"computed","paper":{"title":"Exponents of Zero divisors in the Cohomology ring of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.KT","authors_text":"Jonathan Pakianathan","submitted_at":"2011-12-07T19:45:11Z","abstract_excerpt":"It is well known that the positive degree cohomology of a finite group G is annihilated by |G|. We improve on this bound in the case of odd degree elements in the integer cohomology ring and show that $e_{odd}(G)$, the exponent of the $\\oplus_{k=0}^{\\infty} H^{2k+1}(G,\\mathbb{Z})$ satisfies $e_{odd}(G)^2$ divides 2|G| and in particular $e_{odd}(G) \\leq \\sqrt{2|G|}.$ We also provide examples to show this bound for $e_{odd}(G)$ is sharp as a general bound over all finite groups G.\n  The result comes from a fact about zero divisors having \"complementary exponent\" which we prove using duality in T"},"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":"1112.1671","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-12-07T19:45:11Z","cross_cats_sorted":["math.AT","math.GR"],"title_canon_sha256":"854dc7770f55691624a1f04c5ac048d78c01fb1a11ecb603086a915a91f0dc47","abstract_canon_sha256":"8ecefc2e64a4abe72b0976e88ab46e8cda480af3889acc25a5efd9c456789c6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:45.841343Z","signature_b64":"lU9HZBZkAfPXTFYNLTqBlfU1kp74q99FJJrIUoOinAA/lSFEOFPwyQSmMxicKVEj7n8M9ZH73egSj5HISINgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"880eca22742069a284cff3fc629573b81a0e33014a511af44d328b57d2e405a9","last_reissued_at":"2026-05-18T04:06:45.840735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:45.840735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponents of Zero divisors in the Cohomology ring of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR"],"primary_cat":"math.KT","authors_text":"Jonathan Pakianathan","submitted_at":"2011-12-07T19:45:11Z","abstract_excerpt":"It is well known that the positive degree cohomology of a finite group G is annihilated by |G|. We improve on this bound in the case of odd degree elements in the integer cohomology ring and show that $e_{odd}(G)$, the exponent of the $\\oplus_{k=0}^{\\infty} H^{2k+1}(G,\\mathbb{Z})$ satisfies $e_{odd}(G)^2$ divides 2|G| and in particular $e_{odd}(G) \\leq \\sqrt{2|G|}.$ We also provide examples to show this bound for $e_{odd}(G)$ is sharp as a general bound over all finite groups G.\n  The result comes from a fact about zero divisors having \"complementary exponent\" which we prove using duality in T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1671","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.1671","created_at":"2026-05-18T04:06:45.840821+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1671v2","created_at":"2026-05-18T04:06:45.840821+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1671","created_at":"2026-05-18T04:06:45.840821+00:00"},{"alias_kind":"pith_short_12","alias_value":"RAHMUITUEBU2","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RAHMUITUEBU2FBGP","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RAHMUITU","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA","json":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA.json","graph_json":"https://pith.science/api/pith-number/RAHMUITUEBU2FBGP6P6GFFLTXA/graph.json","events_json":"https://pith.science/api/pith-number/RAHMUITUEBU2FBGP6P6GFFLTXA/events.json","paper":"https://pith.science/paper/RAHMUITU"},"agent_actions":{"view_html":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA","download_json":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA.json","view_paper":"https://pith.science/paper/RAHMUITU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1671&json=true","fetch_graph":"https://pith.science/api/pith-number/RAHMUITUEBU2FBGP6P6GFFLTXA/graph.json","fetch_events":"https://pith.science/api/pith-number/RAHMUITUEBU2FBGP6P6GFFLTXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA/action/storage_attestation","attest_author":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA/action/author_attestation","sign_citation":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA/action/citation_signature","submit_replication":"https://pith.science/pith/RAHMUITUEBU2FBGP6P6GFFLTXA/action/replication_record"}},"created_at":"2026-05-18T04:06:45.840821+00:00","updated_at":"2026-05-18T04:06:45.840821+00:00"}