  Let K be a Cantor set embedded in the real line R. Following Funar and
Neretin, we define the diffeomorphism group of K as the group of homeomorphisms
of K which locally look like a diffeomorphism between two intervals of R.
Higman-Thompson's groups Vn appear as subgroups of such groups. In this
article, we prove some properties of this group. First, we study the Burnside
problem in this group and we prove that any finitely generated subgroup
consisting of finite order elements is finite. This property was already proved
by Rover in the case of the groups Vn. We also prove that any finitely
generated subgroup H without free subsemigroup on two generators is virtually
abelian. The corresponding result for the groups Vn was unknown to our
knowledge. As a consequence, those groups do not contain nilpotent groups which
are not virtually abelian.
