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

Groups of triangular automorphisms of a free associative algebra and a polynomial algebra