  Denote by $G$ the group of interval exchange transformations (IETs) on the
unit interval. Let $G_{per}\subset G$ be the subgroup generated by torsion
elements in $G$ (periodic IETs), and let $G_{rot}\subset G$ be the subset of
2-IETs (rotations).
  The elements of the subgroup $G_1=< G_{per},G_{rot}>\subset G$ (generated by
the sets $G_{per}$ and $G_{rot}$) are characterized constructively in terms of
their Sah-Arnoux-Fathi (SAF) invariant. The characterization implies that a
non-rotation type 3-IET lies in $G_1$ if and only if the lengths of its
exchanged intervals are linearly dependent over $\Q$. In particular,
$G_1\subsetneq G$.
  The main tools used in the paper are the SAF invariant and a recent result by
Y. Vorobets that $G_{per}$ coincides with the commutator subgroup of $G$.
