The width of verbal subgroups in the group of unitriangular matrices over a field. (Q2888834)

Let \(UT_n(K)\) and \(T_n(K)\) be the groups of unitriangular and triangular matrices over a field \(K\). The main purpose in the article under review is to characterize the lattices of verbal subgroups in the above groups. The author determines different equalities between certain subgroups of the group \(UT_n(K)\) and their verbal width. The verbal subgroups in the group \(T_n(K)\) are completely characterized. Going to the case of infinite dimensional matrices, the author proves that every verbal subgroup of the group \(UT(K)\) coincides with a term of the lower central series of this group. Also, some equalities hold for certain verbal subgroups in \(UT(K)\) and their verbal width. The verbal subgroups of \(T(K)\) are also characterized.