Verbal subgroups in the group of triangular matrices over field of characteristic 0

In this paper we describe the verbal subgroups of groups UT_n (K) and T_n (K), which are the groups of, respectively, unitriangular and triangular matrices over field K of characteristic 0. We prove that every verbal subgroup of UT_n (K) coincides with a term of the lower central series of the group and that every verbal subgroup V (T_n (K)) either is of the form V (K) ṡ UT_n (K) or coincides with a verbal subgroup of UT_n (K). We also describe the width of these verbal subgroups and make a few remarks regarding the groups of infinite triangular matrices.