  We study the group IET of all interval exchange transformations. Our first
main result is that the group generated by a generic pairs of elements of IET
is not free (assuming a suitable irreducibility condition on the underlying
permutation). Then we prove that any connected Lie group isomorphic to a
subgroup of IET is abelian.
  Additionally, we show that IET contains no infinite Kazhdan group. We also
prove residual finiteness of finitely presented subgroups of IET and give an
example of a two-generated subgroup of IET of exponential growth that contains
an isomorphic copy of every finite group, and which is therefore not linear.
