{"paper":{"title":"The average size of $3$-torsion in class groups of $2$-extensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jiuya Wang, Melanie Matchett Wood, Robert J. Lemke Oliver","submitted_at":"2021-10-14T21:01:51Z","abstract_excerpt":"We determine the average size of the 3-torsion in class groups of $G$-extensions of a number field when $G$ is any transitive $2$-group containing a transposition, for example $D_4$. It follows from the Cohen--Lenstra--Martinet heuristics that the average size of the $p$-torsion in class groups of $G$-extensions of a number field is conjecturally finite for any $G$ and most $p$ (including $p\\nmid|G|$). Previously this conjecture had only been proven in the cases of $G=S_2$ with $p=3$ and $G=S_3$ with $p=2$. We also show that the average $3$-torsion in a certain relative class group for these $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.07712","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.07712/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}