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⟩isapro-Fgroup} has positive Haar measure. We investigate the properties of F(G) for various choices of F and the influence of F(G) on the structure of G when μ(F(G))>0.
Profinite groups with many elements with large nilpotentizer and generalizations
Andrea Lucchini;Nowras Otmen
2025
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⟩isapro-Fgroup} has positive Haar measure. We investigate the properties of F(G) for various choices of F and the influence of F(G) on the structure of G when μ(F(G))>0.
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