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

  title={Generalized triangle groups, expanders, and a problem of Agol and Wise},
  author={Alexander Lubotzky and Jason Fox Manning and Henry Wilton},
  journal={Commentarii Mathematici Helvetici},
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. 

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