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arXiv · 1411.0469

Nielsen equivalence in Gupta-Sidki groups

Aglaia Myropolska
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Abstract

For a group $G$ generated by $k$ elements, the Nielsen equivalence classes are defined as orbits of the action of $\operatorname{Aut} F_k$, 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 $G_p$.

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Aglaia Myropolska. 2014-11-03. Nielsen equivalence in Gupta-Sidki groups. https://arxiv.org/abs/1411.0469

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