{"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 $3$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3761","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"}