Commuting probability for the Sylow subgroups of a profinite group

Eloisa Detomi, Marta Morigi, Pavel Shumyatsky

Given two subgroups $H,K$ of a compact group $G$, the probability that a random element of $H$ commutes with a random element of $K$ is denoted by $Pr(H,K)$. We show that if $G$ is…