@article{SM_2008_199_4_a1,
author = {Ch. K. Gupta and E. I. Timoshenko},
title = {The test rank of a~soluble product of free {Abelian} groups},
journal = {Sbornik. Mathematics},
pages = {495--510},
year = {2008},
volume = {199},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2008_199_4_a1/}
}
Ch. K. Gupta; E. I. Timoshenko. The test rank of a soluble product of free Abelian groups. Sbornik. Mathematics, Tome 199 (2008) no. 4, pp. 495-510. http://geodesic.mathdoc.fr/item/SM_2008_199_4_a1/
[1] J. Nielsen, “Über die Isomorphismen unendlicher Gruppen ohne Relation”, Math. Ann., 79:3 (1918), 269–272 | DOI | MR | Zbl
[2] H. Zieschang, “Alternierende Produkte in freien Gruppen”, Abh. Math. Sem. Univ. Hamburg, 27 (1964), 13–31 | DOI | MR | Zbl
[3] H. Zieschang, “Über Automorphismen ebener diskontinuierlicher Gruppen”, Math. Ann., 166:2 (1966), 148–167 | DOI | MR | Zbl
[4] G. Rosenberger, “Über Darstellungen von Elementen und Untergruppen in freien Produkten”, Groups–Korea 1983, Proc. Conf. on combinatorial group theory (Kyoungju, Korea, 1983), Lecture Notes in Math., 1098, Springer-Verlag, Berlin, 1984, 142–160 | DOI | MR | Zbl
[5] B. Fine, G. Rosenberger, D. Spellman, M. Stille, “Test words, generic elements and almost primitivity”, Pacific J. Math., 190:2 (1999), 277–297 | MR | Zbl
[6] P. Hill, S. J. Pride, “Commutators, generators and conjugacy equations in groups”, Arch. Math. (Basel), 44:1 (1985), 1–14 | DOI | MR | Zbl
[7] R. N. Kalia, G. Rosenberger, “Automorphisms of the Fuchsian groups op type $(0;2,2,2,q;0)$”, Comm. Algebra, 6:11 (1978), 1115–1129 | DOI | MR | Zbl
[8] N. Gupta, V. Shpilrain, “Nielsen's commutator test for two-generator groups”, Math. Proc. Cambridge Philos. Soc., 114:2 (1993), 295–301 | DOI | MR | Zbl
[9] E. C. Turner, “Test words for automorphisms of free groups”, Bull. London Math. Soc., 28:3 (1996), 255–263 | DOI | MR | Zbl
[10] E. I. Timoshenko, “Test elements and test rank of a free metabelian group”, Siberian Math. J., 41:6 (2000), 1200–1204 | DOI | MR | Zbl
[11] I. V. Chirkov, M. A. Shevelin, “Test sets in free metabelian Lie algebras”, Siberian Math. J., 43:6 (2002), 1135–1140 | DOI | MR | Zbl
[12] Z. Esmerligil, N. Ekici, “Test sets and test rank of a free metabelian Lie algebra”, Comm. Algebra, 31:11 (2003), 5581–5589 | DOI | MR | Zbl
[13] Z. Esmerligil, “Test elements of a free color metabelian Lie superalgebra of rank two”, J. Inst. Math. Comput. Sci. Math. Ser., 17:1 (2004), 25–29 | MR | Zbl
[14] Ch. K. Gupta, E. I. Timoshenko, “Test rank for some free polynilpotent groups”, Algebra Logic, 42:1 (2003), 20–28 | DOI | MR | Zbl
[15] Z. Esmerligil, D. Kahyalar, N. Ekici, “Test rank of $F/R'$ Lie algebras”, Internat. J. Algebra Comput., 16:4 (2006), 817–825 | DOI | MR | Zbl
[16] V. D. Mazurov, E. I. Khukhro (eds.), The Kourovka notebook. Unsolved problems in group theory, ed. 15, Institute of Math., Novosibirsk, 2002 | MR | MR | Zbl | Zbl
[17] V. A. Roman'kov, “Test elements for free solvable groups of rank 2”, Algebra Logic, 40:2 (2001), 106–111 | DOI | MR | Zbl
[18] E. I. Timoshenko, “Computing test rank for a free solvable group”, Algebra Logic, 45:4 (2006), 254–260 | DOI | MR | Zbl
[19] C. K. Gupta, V. A. Roman'kov, E. I. Timoshenko, “Test ranks of free nilpotent groups”, Comm. Algebra, 33:5 (2005), 1627–1634 | DOI | MR | Zbl
[20] Ch. K. Gupta, E. I. Timoshenko, “Criterion for invertibility of endomorphisms and test rank of metabelian products of Abelian groups”, Algebra Logic, 43:5 (2004), 316–326 | DOI | MR | Zbl
[21] R. H. Crowell, R. H. Fox, Introduction to knot theory, Ginn, Boston, MA, 1963 | MR | MR | Zbl | Zbl
[22] V. N. Remeslennikov, V. G. Sokolov, “Some properties of a Magnus embedding”, Algebra Logic, 9:5 (1970), 342–349 | DOI | MR | Zbl
[23] N. Gupta, Free group rings, Contemp. Math., 66, Amer. Math. Soc., Providence, RI, 1987 | MR | Zbl
[24] A. L. Šmel'kin, “On free products of groups”, Math. USSR-Sb., 8:4 (1969), 593–597 | DOI | MR | Zbl
[25] A. L. Shmel'kin, “Some factor groups of a free product”, Topics in modern mathematics. Petrovskiĭseminar, Contemp. Soviet Math., 5, Plenum, New York, 1985, 265–274 | MR | MR | Zbl
[26] N. S. Romanovskii, “Shmel'kin embeddings for abstract and profinite groups”, Algebra Logic, 38:5 (1999), 326–334 | DOI | MR | Zbl
[27] C. K. Gupta, N. S. Romanovski, “On torsion in factors of polynilpotent series of a group with a single relation”, Internat. J. Algebra Comput., 14:4 (2004), 513–523 | DOI | MR | Zbl