{"paper":{"title":"Classes of order 4 in the strict class group of number fields and remarks on unramified quadratic extensions of unit type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David S. Dummit","submitted_at":"2018-11-13T21:38:00Z","abstract_excerpt":"Let $K$ be a number field of degree $n$ over ${\\mathbb Q}$. Then the 4-rank of the strict class group of $K$ is at least ${\\text{rank}_2 \\, } ({ E_{K}^{+} } / E_K^2) - \\lfloor n /2 \\rfloor$ where $E_K$ and ${ E_{K}^{+} }$ denote the units and the totally positive units of $K$, respectively, and $\\text{rank}_2$ is the dimension as an elementary abelian 2-group. In particular, the strict class group of a totally real field $K$ with a totally positive system of fundamental units contains at least$(n-1)/2$ ($n$ odd) or $n/2 -1$ ($n$ even) independent elements of order 4. We also investigate when u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05535","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"}