On two-generator subgroups in SL_2(Z), SL_2(Q), and SL_2(R)
  We consider what some authors call 'parabolic M\"obius subgroups' of matrices over Z, Q, and R and focus on the membership problem in these subgroups and complexity of relevant algorithms. 
Anastasiia Chorna, Katherine Geller, and Vladimir Shpilrain
math.GR