## Abstract

At the 2011 Durham Conference "Geometry and Arithmetic of Lattices" M. Kapovich formulated the following Question. Does there exist an embedding ℤ^{2} * ℤ Rightwards arrow with hook sign SL(3, ℤ)? The goal of the paper is to prove the following Main Theorem. If p and m are arbitrary positive integers then there exists an embedding ℤ^{2} * F_{m} Rightwards arrow with hook sign SL(3, ℤ[1/p]).

Original language | English |
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Article number | 1250057 |

Journal | International Journal of Algebra and Computation |

Volume | 22 |

Issue number | 7 |

DOIs | |

State | Published - Nov 2012 |

### Bibliographical note

Funding Information:The author would like to thank several institutions and foundations for their support: SFB 701 “Spektrale Strukturen und Topologische Methoden in der Mathe-matik”, USA-Israel Binational Science foundation under BSF grant 2004010, the Emmy Noether Research Institute for Mathematics, Bar-Ilan University and the Israel Science Foundation under ISF grant 657/09 and Max Planck Institute for Mathematics, Bonn. I would like to thank the referees for very helpful suggestions and comments.

## Keywords

- Arithmetic subgroups
- free products
- free subgroups
- lattices

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