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

2017/02/27 by Lubotzky, Alexander, Manning, Jason Fox, Wilton, Henry · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1702.08200

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.

Cited by

• Automaticity of non-positively curved k-fold triangle groups

Related

• Groups that produce expander graphs
• Generalised Triangle Groups of Type (2,4,2)
• Symmetric Groups and Expander Graphs
• Expansion in simple groups
• Expansion in Cayley graphs, Cayley sum graphs and their twists