{"paper":{"title":"Nielsen equivalence in a class of random groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Richard Weidmann","submitted_at":"2013-09-28T13:21:39Z","abstract_excerpt":"We show that for every $n\\ge 2$ there exists a torsion-free one-ended word-hyperbolic group $G$ of rank $n$ admitting generating $n$-tuples $(a_1,\\ldots ,a_n)$ and $(b_1,\\ldots ,b_n)$ such that the $(2n-1)$-tuples $$(a_1,\\ldots ,a_n, \\underbrace{1,\\ldots ,1}_{n-1 \\text{times}})\\hbox{ and }(b_1,\\ldots, b_n, \\underbrace{1,\\ldots ,1}_{n-1 \\text{times}})$$ are not Nielsen-equivalent in $G$. The group $G$ is produced via a probabilistic construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7458","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"}