Profinite groups with many elements with large nilpotentizer and generalizations

2025/05/22 by Martino Garonzi, Garonzi, Martino, Andrea Lucchini +3
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2505.16589

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a profinite group G and a family F of finite groups closed under taking subgroups, direct products and quotients, denote by F(G) the set of elements g ∈ G such that \x ∈ G | ⟨ g,x ⟩ is a pro-F group\ has positive Haar measure. We investigate the properties of F(G) for various choices of F and its influence on the structure of G.

Citations

• Probabilistic Generation of Finite Almost Simple Groups
• Words, Hausdorff dimension and randomly free groups
• Non-nilpotent graph of a group

Related

• The Haar measure of a profinite n-ary group
• Probabilistic properties of profinite groups
• Some aspects of profinite group theory
• Profinite groups with many elements of bounded order
• Algebraic properties of profinite groups