{"paper":{"title":"A remark On Abelianized Absolute Galois Group of Imaginary Quadratic Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bart de Smit, Pavel Solomatin","submitted_at":"2017-03-21T14:36:23Z","abstract_excerpt":"The main purpose of this paper is to extend results on isomorphism types of the abelianized absolute Galois group $\\mathcal G_K^{ab}$, where $K$ denotes imaginary quadratic field. In particular, we will show that if the class number $h_K$ of an imaginary quadratic field $K$ different from $\\mathbb Q(i)$, $\\mathbb Q(\\sqrt{-2})$ is a fixed prime number $p$ then there are only two isomorphism types of $\\mathcal G_K^{ab}$ which could occur. For instance, this result implies that imaginary quadratic fields of the discriminant $D_K$ belonging to the set $\\{-35, -51, -91, -115, -123, -187, -235,$ $ -"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07241","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"}