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Mayer, Mohammed Taous","submitted_at":"2014-04-14T21:37:07Z","abstract_excerpt":"Let $p_1\\equiv p_2\\equiv -q\\equiv1 \\pmod4$ be different primes such that $\\displaystyle\\left(\\frac{2}{p_1}\\right)= \\displaystyle\\left(\\frac{2}{p_2}\\right)=\\displaystyle\\left(\\frac{p_1}{q}\\right)=\\displaystyle\\left(\\frac{p_2}{q}\\right)=-1$. Put $d=p_1p_2q$ and $i=\\sqrt{-1}$, then the bicyclic biquadratic field ${k}=\\mathbb{Q}(\\sqrt{d},i)$ has an elementary abelian $2$-class group, $\\mathbf{C}l_2(k)$, of rank $3$. In this paper, we study the principalization of the $2$-classes of ${k}$ in its fourteen unramified abelian extensions $\\mathbb{K}_j$ and $\\mathbb{L}_j$ within ${k}_2^{(1)}$, that is 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":"1404.3761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-14T21:37:07Z","cross_cats_sorted":[],"title_canon_sha256":"5f31e2da17e41b79f25c097c7be307b9c55b9b1b2c0adbf1942b8776bc8dafed","abstract_canon_sha256":"f4d2318246fa7cd209ce2c0500be6ecf7330c5d8fcbbf34f7a16d4ed67d14549"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:13.705437Z","signature_b64":"AIC6uCfQU7Zu7lPfQxbZbn3oKQJ58vC+ydFhH56IcRpzATRVLTG87wIhztPMdR9mw3e1nzNexlhphLinJmLIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88343234010e0488e0936a1aa007668f6095dbf4145f8541b26c565d79364060","last_reissued_at":"2026-05-18T02:54:13.704897Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:13.704897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Principalization of $2$-class groups of type $(2,2,2)$ of biquadratic fields $\\mathbb{Q}\\left(\\sqrt{\\strut p_1p_2q},\\sqrt{\\strut -1}\\right)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abdelkader Zekhnini, Abdelmalek Azizi, Daniel C. Mayer, Mohammed Taous","submitted_at":"2014-04-14T21:37:07Z","abstract_excerpt":"Let $p_1\\equiv p_2\\equiv -q\\equiv1 \\pmod4$ be different primes such that $\\displaystyle\\left(\\frac{2}{p_1}\\right)= \\displaystyle\\left(\\frac{2}{p_2}\\right)=\\displaystyle\\left(\\frac{p_1}{q}\\right)=\\displaystyle\\left(\\frac{p_2}{q}\\right)=-1$. Put $d=p_1p_2q$ and $i=\\sqrt{-1}$, then the bicyclic biquadratic field ${k}=\\mathbb{Q}(\\sqrt{d},i)$ has an elementary abelian $2$-class group, $\\mathbf{C}l_2(k)$, of rank $3$. 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