Abstract
We computed the test rank of a free solvable Lie algebra of finite rank.
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Timoshenko E. I., “Test elements and test rank of a free metabelian group,” Siberian Math. J., 41, No. 6, 1200–1204 (2000).
Chirkov I. V. and Shevelin M. A., “Test sets in free metabelian Lie algebras,” Siberian Math. J., 43, No. 6, 1135–1140 (2002).
Esmerligil Z. and Ekici N., “Test sets and test rank of a free metabelian Lie algebra,” Comm. Algebra, 31, No. 11, 5581–5589 (2003).
Esmerligil Z., “Test elements of a free color metabelian Lie superalgebra of rank two,” J. Inst. Math. Comput. Sci. Math. Ser., 17, No. 1, 25–29 (2004).
Gupta Ch. K. and Timoshenko E. I., “Test rank for some free polynilpotent groups,” Algebra and Logic, 42, No. 1, 20–28 (2003).
Esmerligil Z., Kahyalar D., and Ekici N., “Test rank of F/R’ Lie algebras,” Internat. J. Algebra Comput., 16, No. 4, 817–825 (2006).
The Kourovka Notebook. Unsolved Problems in Group Theory. Vol. 15, Inst. Math. (Novosibirsk), Novosibirsk (2002).
Timoshenko E. I., “Computing test rank for a free solvable group,” Algebra and Logic, 45, No. 4, 254–260 (2006).
Bokut’ L. A., “A base of free polynilpotent Lee algebras,” Algebra i Logika, 2, No. 4, 13–20 (1963).
Kharlampovich O. G., “The Lyndon condition for solvable Lie algebras,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 9, 50–59 (1984).
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Original Russian Text Copyright © 2008 Timoshenko E. I. and Shevelin M. A.
The first author was supported by the Russian Foundation for Basic Research (Grant 05.01.00292).
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Novosibirsk; Omsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1420–1426, November–December, 2008.
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Timoshenko, E.I., Shevelin, M.A. Computing the test rank of a free solvable Lie algebra. Sib Math J 49, 1131–1135 (2008). https://doi.org/10.1007/s11202-008-0109-6
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DOI: https://doi.org/10.1007/s11202-008-0109-6