TY - JOUR
T1 - Simultaneous ping-pong Partners in PSLn(ℤ)
AU - Soifer, G.
AU - Vishkautsan, S.
PY - 2009
Y1 - 2009
N2 - 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).
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).
KW - Hyperbolic
KW - Projective transformation
KW - Proximal element
UR - http://www.scopus.com/inward/record.url?scp=77950927737&partnerID=8YFLogxK
U2 - 10.1080/00927870802570719
DO - 10.1080/00927870802570719
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:77950927737
SN - 0092-7872
VL - 38
SP - 288
EP - 301
JO - Communications in Algebra
JF - Communications in Algebra
IS - 1
ER -