{"paper":{"title":"On some metabelian 2-group whose abelianization is of type (2, 2, 2) and applications","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Abdelkader Zekhnini, Abdelmalek Azizi, Mohammed Taous","submitted_at":"2015-03-05T23:00:06Z","abstract_excerpt":"Let $G$ be some metabelian $2$-group satisfying the condition $G/G'\\simeq \\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/2\\mathbb{Z}$. In this paper, we construct all the subgroups of $G$ of index $2$ or $4$, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem of the $2$-ideal classes of some fields $\\mathbf{k}$ satisfying the condition $\\mathrm{G}al(\\mathbf{k}_2^{(2)}/\\mathbf{k})\\simeq G$, where $\\mathbf{k}_2^{(2)}$ is the second Hilbert $2$-class field of $\\mathbf{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01813","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"}