## Abstract

We show that for any finite set F of nonidentity elements in PSL_{n}(ℤ) for n ≥ 3, consisting of hyperbolic, finite order, or unipotent elements, there exists an element g of infinite order in PSL_{n}(ℤ) such that for any h ∈ F, the subgroup 〈g, h〉 generated by g and h is canonically isomorphic to the free product 〈g〉 * 〈h〉. We also show that the set of such elements in PSL_{n}(ℤ) is Zariski dense in PSL_{n}(ℝ).

Original language | English |
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Pages (from-to) | 288-301 |

Number of pages | 14 |

Journal | Communications in Algebra |

Volume | 38 |

Issue number | 1 |

DOIs | |

State | Published - 2009 |

## Keywords

- Hyperbolic
- Projective transformation
- Proximal element

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