An (FA)-group that is not (FR)
  We construct examples of finitely generated groups L that have non-trivial actions on $\mathbb{R}$-trees but which cannot act, without fixing a vertex, on any simplicial tree. Moreover, any finitely presented group mapping onto L does have a fixed point-free action on some simplicial tree. 
Martin J. Dunwoody and Ashot Minasyan
math.GR math.GT