2013/09/30 by Ilya Kapovich, Richard Weidmann · 2 citations
Computer Science · Mathematics · #Class (philosophy) #Combinatorics #Computer science #Discrete mathematics #Equivalence (formal languages) #Free group #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Mathematical Dynamics and Fractals #Mathematics #Rank (graph theory) #Torsion (gastropod) #Tuple #Word (group theory) #math.GR #math.GT #semigroups and automata theory
paper · pdf · doi:10.1112/jtopol/jtw001
published in Journal of Topology 9(2), 502-534 (Wiley) · 34 pages, 2 figures; a revised final version, to appear in the Journal of Topology
arxiv created 2016/01/12 · openalex publication_date 2016/05/06 · arxiv updated 2016/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that, for every n ⩾ 2 , there exists a torsion-free one-ended word-hyperbolic group G of rank n admitting generating n-tuples ( a 1 , … , a n ) and ( b 1 , … , b n ) such that the ( 2 n - 1 ) -tuples ( a 1 , … , a n , 1 , … , 1 ︸ n - 1 times ) and ( b 1 , … , b n , 1 , … , 1 ︸ n - 1 times ) are not Nielsen equivalent in G. The group G is produced via a probabilistic construction.