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