  We study a structure of the group of unitriangular automorphisms of a free
associative algebra and a polynomial algebra and prove that this group is a
semi direct product of abelian groups. Using this decomposition we describe a
structure of the lower central series and the series of derived subgroups for
the group of unitriangular automorphisms and prove that every element from the
derived subgroup is a commutator. In addition we prove that the group of
unitriangular automorphisms of a free associative algebra of rang more than 2
is not linear and describe some two-generated subgroups from these group. Also
we give a more simple system of generators for the group of tame automorphisms
than the system from Umirbaev's paper.
