Nielsen equivalence in Gupta-Sidki groups

2014/11/03 by Aglaia Myropolska, Myropolska, Aglaia
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.GR

paper · pdf · doi:10.48550/arxiv.1411.0469

arxiv created 2014/11/03 · openalex publication_date 2014/11/03 · arxiv updated 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a group G generated by k elements, the Nielsen equivalence classes are defined as orbits of the action of Aut F_k, the automorphism group of the free group of rank k, on the set of generating k-tuples of G. Let p≥ 3 be prime and G_p the Gupta-Sidki p-group. We prove that there are infinitely many Nielsen equivalence classes on generating pairs of G_p.

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