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

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.

12 pages, 2 figures. V2 incorporates changes suggested by the referee. This is the final version accepted for publication