Profinite groups with many elements with large nilpotentizer and generalizations
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.
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