Geodesic
Computing Test Rank for a Free Solvable Group
Algebra i logika, Tome 45 (2006) no. 4, pp. 447-457

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that test rank of a free solvable non-Abelian group of finite rank is 1 less than the rank of that group. This gives the answer to Question 14.88 posed in the Kourovka Notebook by Fine and Shpilrain, asking whether or not a free solvable group of rank 2 and solvability index $n\geqslant3$ has test elements.
Keywords: free solvable group
Mots-clés : test element. 
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     author = {E. I. Timoshenko},
     title = {Computing {Test} {Rank} for a {Free} {Solvable} {Group}},
     journal = {Algebra i logika},
     pages = {447--457},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2006_45_4_a4/}
}
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E. I. Timoshenko. Computing Test Rank for a Free Solvable Group. Algebra i logika, Tome 45 (2006) no. 4, pp. 447-457. http://geodesic.mathdoc.fr/item/AL_2006_45_4_a4/