{"paper":{"title":"Rationality problems for relation modules of dihedral groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.GR"],"primary_cat":"math.NT","authors_text":"Aiichi Yamasaki, Akinari Hoshi, Ming-chang Kang","submitted_at":"2015-03-16T07:14:36Z","abstract_excerpt":"Let D_n be the dihedral group of order 2n where n \\ge 2, 1 \\to R \\to F \\to D_n \\to 1 be a free presentation of D_n. R^{ab}:=R/[R,R] becomes a \\bm{Z}[D_n]-lattice. We will study the module structure and the rationality problem of R^{ab}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04543","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":""},"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"}