Invariable generation of prosoluble groups

2014/10/20 by Eloisa Detomi, Detomi, Eloisa, Andrea Lucchini +1
Computer Science · Mathematics · #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.GR

paper · pdf · doi:10.48550/arxiv.1410.5271

openalex publication_date 2014/10/20 · arxiv created 2014/10/21 · arxiv updated 2014/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A group G is invariably generated by a subset S of G if G= s^g(s) | s∈ S for each choice of g(s) ∈ G, s ∈ S. Answering two questions posed by Kantor, Lubotzky and Shalev, 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.

Citations

• Invariable generation with elements of coprime prime-power order
• Invariable Generation of Infinite Groups

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