Profinite groups with many commuting pairs or involutions
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We prove that if the set of commuting pairs of a profinite group G has positive Haar measure then G is abelian by finite. Using this we show that the set I of involutions has positive measure exactly if I contains a nonempty open subset of G.
KeywordsOpen Subset Positive Measure Haar Measure Nonempty Open Subset Profinite Group
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