{"paper":{"title":"An Outer Commutator Multiplier and Capability of Finitely Generated Abelian Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Behrooz Mashayekhy, Mohsen Parvizi","submitted_at":"2010-12-15T08:22:34Z","abstract_excerpt":"We present an explicit structure for the Baer invariant of a finitely generated abelian group with respect to the variety $[\\mathfrak{N}_{c_1},\\mathfrak{N}_{c_2}]$, for all $c_2\\leq c_1\\leq 2c_2$. As a consequence we determine necessary and sufficient conditions for such groups to be $[\\mathfrak{N}_{c_1},\\mathfrak{N}_{c_2}]$-capable. We also show that if $c_1\\neq 1\\neq c_2$, then a finitely generated abelian group is $[\\mathfrak{N}_{c_1},\\mathfrak{N}_{c_2}]$-capable if and only if it is capable. Finally we show that $\\mathfrak{S}_2$-capability implies capability but there is a finitely generat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3244","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"}