Citation
L. Levai et L. Pyber, Profinite groups with many commuting pairs or involutions, ARCH MATH, 75(1), 2000, pp. 1-7
Citations number
14
Categorie Soggetti
Mathematics
Journal title
ARCHIV DER MATHEMATIK
ISSN journal
0003889X
→ ACNP
Volume
75
Issue
1
Year of publication
2000
Pages
1 - 7
Database
ISI
SICI code
0003-889X(20000703)75:1<1:PGWMCP>2.0.ZU;2-G
Abstract
We prove that if the set of commuting pairs of a profinite group G has posi
tive 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.