Nielsen equivalence in Gupta-Sidki groups

Aglaia Myropolska

paper

Nielsen equivalence in Gupta-Sidki groups

arXiv:1411.0469

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 $p \geq 3$ be prime and $G_{p}$ the Gupta-Sidki $p$ -group. We prove that there are infinitely many Nielsen equivalence classes on generating pairs of $G_{p}$ .