Profinite groups with many commuting pairs or involutions |
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| Authors: | L Lévai L Pyber |
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| Institution: | (1) Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;(2) Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA; |
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| Abstract: | 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. |
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