Geodesic
Test Rank for Some Free Polynilpotent Groups
Algebra i logika, Tome 42 (2003) no. 1, pp. 37-50

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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 $c\geqslant 2$.
Keywords: test rank, polynilpotent group, free group. 
@article{AL_2003_42_1_a2,
     author = {Ch. K. Gupta and E. I. Timoshenko},
     title = {Test {Rank} for {Some} {Free} {Polynilpotent} {Groups}},
     journal = {Algebra i logika},
     pages = {37--50},
     publisher = {mathdoc},
     volume = {42},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2003_42_1_a2/}
}
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Ch. K. Gupta; E. I. Timoshenko. Test Rank for Some Free Polynilpotent Groups. Algebra i logika, Tome 42 (2003) no. 1, pp. 37-50. http://geodesic.mathdoc.fr/item/AL_2003_42_1_a2/