Dovghei Z. Structure of triangle automorphisms of the two variable polynomial ring over the set field

We study of structure of triangle automorphisms of the two variable polynomial ring over the set field. Group properties are described of groups triangle automorphism are investigational for the fields of a zero characteristic and groups of unitriangle automorphism rings of polynomials from two variables over a field of characteristic are investigated. Groups of unitriangle automorphism, and triangle automorphism - for the fields a zero characteristic and characteristic , in particular eventual fields. We describe main properties of the unitriangle automorphism group of the polynomial algebra over a field the characteristic 0. The lower and upper central series and conjugate classes of this group are characterized. the lattice of it's verbal subgroup is described. A basic properties of the unitriangle automorphism group of the two variable polynomial ring over a field of characteristic are investigated. We characterize the -power werbal subgroup, found its width and we estimate the Engel length of the unitriangle automorphism group.