{"paper":{"title":"Torsion cohomology for solvable groups of finite rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.GR","authors_text":"Karl Lorensen","submitted_at":"2014-06-14T13:49:48Z","abstract_excerpt":"We define a class $\\mathcal{U}$ of solvable groups of finite abelian section rank which includes all such groups that are virtually torsion-free as well as those that are finitely generated. Assume that $G$ is a group in $\\mathcal{U}$ and $A$ a $\\mathbb ZG$-module. If $A$ is $\\mathbb Z$-torsion-free and has finite $\\mathbb Z$-rank, we stipulate a condition on $A$ that guarantees that $H^n(G,A)$ and $H_n(G,A)$ must be finite for $n\\geq 0$. Moreover, if the underlying abelian group of $A$ is a \\v{C}ernikov group, we identify a similar condition on $A$ that ensures that $H^n(G,A)$ must be a \\v{C}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3731","kind":"arxiv","version":3},"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"}