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Aug 21, 2012 at 1:55 comment added Colin Reid Interesting. I was not aware of the term 'Hecke pair'. I should also cite Schlichting's 1979 article in my document on the arXiv.
Aug 20, 2012 at 18:41 comment added user23860 In the context of noncommutative geometry and operator algebras, commensurated subgroups are called almost normal. Regarding your question about the possibility of a T.D.L.C. approach to this class of subgroups, you may find some interesting notions and discussion in Tzanev's paper, titled "Hecke C*-algebras and amenability", J. Operator Theory, 50, (2003), 169–178.
Aug 20, 2012 at 2:38 history edited Colin Reid CC BY-SA 3.0
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Aug 20, 2012 at 2:19 history asked Colin Reid CC BY-SA 3.0