A group G is invariably generated by a subset S of G if G = 〈sg(s) | s ∈ S〉 for each choice of g(s) ∈ G, s ∈ S. Answering two questions posed by Kantor, Lubotzky and Shalev in [8], we prove that the free prosoluble group of rank d ≥ 2 cannot be invariably generated by a finite set of elements, while the free solvable profinite group of rank d and derived length l is invariably generated by precisely l(d − 1) + 1 elements. © 2016, Hebrew University of Jerusalem.

Invariable generation of prosoluble groups

DETOMI, ELOISA MICHELA;LUCCHINI, ANDREA
2016

Abstract

A group G is invariably generated by a subset S of G if G = 〈sg(s) | s ∈ S〉 for each choice of g(s) ∈ G, s ∈ S. Answering two questions posed by Kantor, Lubotzky and Shalev in [8], we prove that the free prosoluble group of rank d ≥ 2 cannot be invariably generated by a finite set of elements, while the free solvable profinite group of rank d and derived length l is invariably generated by precisely l(d − 1) + 1 elements. © 2016, Hebrew University of Jerusalem.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3199297
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