Archiv der Mathematik

, Volume 75, Issue 1, pp 1–7 | Cite as

Profinite groups with many commuting pairs or involutions

  • L. Lévai
  • L. Pyber

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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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • L. Lévai
    • 1
  • L. Pyber
    • 1
  1. 1.Alfrèd Rènyi Institute of Mathematics, Hungarian Academy of Sciences, P.O.B. 127, H-1364 Budapest, HungaryHU

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