Emerging Applications of Number Theory

Volume 109 of the series The IMA Volumes in Mathematics and its Applications pp 571-581

Expander Graphs and Amenable Quotients

  • Yehuda ShalomAffiliated withInstitute of Mathematics, Hebrew University

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We continue the search, carried out in [Sh1], for new sets of generators for families of finite groups (such as S L 2(F P )), which make the corresponding Cayley graphs an expander family. Along the way to our new result, we survey some of the recent results and methods introduced in [Sh1], based on the use of invariant means on the profinite completion of the finite groups.