  We study a generalization Rec_d of the group IET=Rec_1 of interval exchange
transformations in every dimension d>0, called the rectangle exchange
transformations group. The subset of restricted rotations in IET is a
generating subset and we prove that a natural generalization of these elements,
called restricted shuffles, form a generating subset of Rec_d. We denote by T_d
the subset of Rec_d made up of those transformations that permute two disjoint
rectangles by translations. We prove that the derived subgroup of Rec_d is
generated by T_d. We also identify the abelianization of Rec_d.
