arXiv subjects
Publications and source records attributed to E. I. Timoshenko.
We construct an ordered set of commutators in a partially commutative nilpotent group $F(X; Γ; \mathfrak N_m)$. This set allows us to define a canonical form for each element of $F(X; Γ; \mathfrak N_m)$. Namely, we construct a Maltsev basis for the group $F(X; Γ; \mathfrak N_m).$
We study verbally closed subgroups of free solvable groups. A number of results is proved that give sufficient conditions under whose a verbally closed subgroup is turned to be a retract and so algebraically closed of the full group.
We prove that every verbally closed two-generated subgroup of a free solvable group G of a finite rank is a retract of G.