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Nielsen equivalence in Gupta-Sidki groups


Author: Aglaia Myropolska
Journal: Proc. Amer. Math. Soc. 145 (2017), 3331-3342
MSC (2010): Primary 20E05, 20E36, 20F05
DOI: https://doi.org/10.1090/proc/13612
Published electronically: April 6, 2017
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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 $ \textrm {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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Additional Information

Aglaia Myropolska
Affiliation: Financial Engineering, École Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland

DOI: https://doi.org/10.1090/proc/13612
Received by editor(s): May 29, 2015
Received by editor(s) in revised form: September 20, 2016
Published electronically: April 6, 2017
Additional Notes: The author acknowledges the support of the Swiss National Science Foundation, grant 200021_144323
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2017 American Mathematical Society