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We answer this question negatively by calculating the relative group cohomology $\\cF H^* (G, \\bbF_2)$ where $G=\\bbZ/2\\times \\bbZ /2$ and $\\cF$ is the family of cyclic subgroups of $G$. To do this calculation we first observe that the relative group cohomology $\\cF H^*(G, M)$ can be calculated using "},"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":"1205.1120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-05-05T11:26:25Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"fb3fd4df851a91c0d94772751eb6c5c9dd8b879c3af27eb793d2334e01a2fb46","abstract_canon_sha256":"8cd8c9298646483d6a6b1ab9adf48f071b3ef15cb1815ceb85d67599949b86d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:12.057334Z","signature_b64":"bV7oQT7j5SfbeQtz5gw+NbAoLg+TQQr84AjaF8quN1W6e7Rae9E3WLz5rc4YOTAUwFjPua+s9PpBodFL9G3MCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"883a6a757c38054e6e501735938b8e2cf8176a91215e79d189ef2a9432ee2de4","last_reissued_at":"2026-05-18T03:56:12.056629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:12.056629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relative group cohomology and the orbit category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AT","authors_text":"Ergun Yalcin, Semra Pamuk","submitted_at":"2012-05-05T11:26:25Z","abstract_excerpt":"Let $G$ be a finite group and $\\cF$ be a family of subgroups of $G$ closed under conjugation and taking subgroups. 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