Test Rank for Some Free Polynilpotent Groups

We prove a theorem on possible test rank values for groups of the form $F/R'$. It is shown that test rank of a free polynilpotent group $F_r(\mathbb{A}\mathbb{N}_{c_1}\ldots\mathbb{N}_{c_l})$ is equal to $r-1$ or $r$, for any $r \geqslant 2$ and every collection $(c_1,\ldots,c_l)$ of classes. Moreover, $tr(F_r(\mathbb{A}\mathbb{N}_c))=r-1$ for $r\geqslant 2$ and $c\geqslant 2$.