Nielsen equivalence in a class of random groups

Abstract

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 $(a_1,\dots ,a_n)$ and $(b_1,\dots ,b_n)$ such that the $(2n-1)$-tuples $$(a_1,\dots ,a_n,\underset{n-1\text{times}}{\underbrace{1,\dots ,1}})and(b_1,\dots ,b_n,\underset{n-1\text{times}}{\underbrace{1,\dots ,1}})$$ are not Nielsen-equivalent in $G$. The group $G$ is produced via a probabilistic construction.

34 pages, 2 figures; a revised final version, to appear in the Journal of Topology

References in corpus (2)

• Conformal dimension and random groups
• Nielsen equivalence in small cancellation groups

Cited by in corpus (1)

• Nielsen Equivalence in Fuchsian groups