JournalscmhVol. 94, No. 1pp. 53–66

Generalized triangle groups, expanders, and a problem of Agol and Wise

  • Alexander Lubotzky

    Hebrew University, Jerusalem, Israel

  • Jason Fox Manning

    Cornell University, Ithaca, USA

  • Henry Wilton

    University of Cambridge, UK
Generalized triangle groups, expanders, and a problem of Agol and Wise cover
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Abstract

Answering a question asked by Agol and Wise, we show that a desired stronger form of Wise’s malnormal special quotient theorem does not hold. The counterexamples are generalizations of triangle groups, built using the Ramanujan graphs constructed by Lubotzky–Phillips–Sarnak.

Cite this article

Alexander Lubotzky, Jason Fox Manning, Henry Wilton, Generalized triangle groups, expanders, and a problem of Agol and Wise. Comment. Math. Helv. 94 (2019), no. 1, pp. 53–66

DOI 10.4171/CMH/454