Abstract:
In this paper conditions are obtained for the residual finiteness with respect to conjugacy of groups of the form $F/R_k$, where $F$ is a free group, $R\triangleleft F$, and $R_k$ is the $k$th term of the lower central series of $R$. It is shown that free polynilpotent groups are residually finite with respect to conjugacy.
The proof utilizes an embedding of groups of the form $F/R_k$ into a twisted wreath product of simpler groups. Properties of this embedding are also studied.
Bibliography: 12 titles.