{"paper":{"title":"Capitulation des 2-classes d'id\\'eaux de $\\mathbf{k}=\\mathbb{Q}(\\sqrt{2p}, i)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abdelmalek Azizi, Mohammed Taous","submitted_at":"2014-02-06T02:07:58Z","abstract_excerpt":"Let $p$ be a prime number such that $p\\equiv 1$ mod $8$ and $i=\\sqrt{-1}$. Let $\\mathbf{k}=\\mathbb{Q}(\\sqrt{2p}, i)$, $\\mathbf{k}_1^{(2)}$ be the Hilbert $2$-class field of $\\mathbf{k}$, $\\mathbf{k}_2^{(2)}$ be the Hilbert $2$-class field of $\\mathbf{k}_1^{(2)}$ and $G=\\mathrm{Gal}(\\mathbf{k}_2^{(2)}/\\mathbf{k})$ be the Galois group of $\\mathbf{k}_2^{(2)}/\\mathbf{k}$. Suppose that the $2$-part, $C_{\\mathbf{k}, 2}$, of the class group of $\\mathbf{k}$ is of type $(2, 4)$; then $\\mathbf{k}_1^{(2)}$ contains six extensions $\\mathbf{K_{i, j}}/\\mathbf{k}$, $i=1, 2, 3$ and $j=2, 4$. Our goal is to st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1228","kind":"arxiv","version":1},"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"}