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The main goal of this paper is to study the extensions F(G)/F given that F contains enough roots of unity and determine how close they are to being purely transcendental.\n  In particular we show that F(G)/F is a stably rational extension for $G = C_2 \\times C_{2n}"},"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":"1401.4717","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-19T18:53:22Z","cross_cats_sorted":[],"title_canon_sha256":"0574b8b3a98ee81c88841ba1a15b4ebdab1ebcc3cd5c48c6cb4988b7b1f9187c","abstract_canon_sha256":"0284d08399ba45e60f55206ac455f514183760a0cc4c14bdcc65750306dfa534"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:08.643445Z","signature_b64":"CECIADYmRB0akI5pP+pP37883IAOLoftzBA06lAWEoS+njRRU1b3i9JLgWO4G9FLfbnZGKtPoAvDf0Hy+DVXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df6822b330281d80c596ba360b0a53660798f102e69730abca11a5290c6bb3fd","last_reissued_at":"2026-05-18T00:41:08.642969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:08.642969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The center of the generic G-crossed product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ofir David","submitted_at":"2014-01-19T18:53:22Z","abstract_excerpt":"Let G be a finite group and let F be a field of characteristic zero. 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