Simultaneous ping-pong Partners in PSLn(ℤ)

G. Soifer; S. Vishkautsan

doi:10.1080/00927870802570719

Simultaneous ping-pong Partners in PSL_n(ℤ)

G. Soifer
, S. Vishkautsan

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	288-301
Number of pages	14
Journal	Communications in Algebra
Volume	38
Issue number	1
DOIs	https://doi.org/10.1080/00927870802570719
State	Published - 2009

Keywords

Hyperbolic
Projective transformation
Proximal element

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10.1080/00927870802570719

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AB - We show that for any finite set F of nonidentity elements in PSLn(ℤ) for n ≥ 3, consisting of hyperbolic, finite order, or unipotent elements, there exists an element g of infinite order in PSLn(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 PSLn(ℤ) is Zariski dense in PSLn(ℝ).

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KW - Projective transformation

KW - Proximal element

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Simultaneous ping-pong Partners in PSL_n(ℤ)

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Keywords

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