{"paper":{"title":"Subgroups of direct products of elementarily free groups","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"James Howie, Martin R Bridson","submitted_at":"2005-06-23T17:14:34Z","abstract_excerpt":"We exploit Zlil Sela's description of the structure of groups having the same elementary theory as free groups: they and their finitely generated subgroups form a prescribed subclass E of the hyperbolic limit groups.\n  We prove that if $G_1,...,G_n$ are in E then a subgroup $\\Gamma\\subset G_1\\times...\\times G_n$ is of type $\\FP_n$ if and only if $\\Gamma$ is itself, up to finite index, the direct product of at most $n$ groups from $\\mathcal E$. This answers a question of Sela."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506482","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"}