Simultaneous ping-pong Partners in PSLn(ℤ)

G. Soifer, S. Vishkautsan

Research output: Contribution to journalArticlepeer-review

Abstract

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).

Original languageEnglish
Pages (from-to)288-301
Number of pages14
JournalCommunications in Algebra
Volume38
Issue number1
DOIs
StatePublished - 2009

Keywords

  • Hyperbolic
  • Projective transformation
  • Proximal element

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