# Hyperbolic generalized triangle groups, property (T) and finite simple quotients

@article{Caprace2022HyperbolicGT, title={Hyperbolic generalized triangle groups, property (T) and finite simple quotients}, author={Pierre‐Emmanuel Caprace and Marston D. E. Conder and Marek Kaluba and Stefan Witzel}, journal={Journal of the London Mathematical Society}, year={2022} }

We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those hyperbolic Kazhdan groups possess finite simple quotient groups of arbitrarily large rank; they constitute the first known specimens combining those properties. All the hyperbolic groups we consider are non-positively curved k-fold generalized triangle groups…

## One Citation

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. We construct new families of groups with property (T) and inﬁn- itely many alternating group quotients. One of those consists of subgroups of Aut( F p [ x 1 ,...,x n ]) generated by a suitable set…

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