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. 53–66DOI 10.4171/CMH/454