Geodesic
On the Engel problem
Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 53-62 
S. P. Mishchenko. On the Engel problem. Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 53-62. http://geodesic.mathdoc.fr/item/SM_1985_52_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that a variety of Lie algebras over a field of characteristic zero satisfying an Engel condition of bounded index and for which the growth of the codimensions of the verbal ideal is at most exponential is nilpotent. Bibliography: 8 titles.

[1] Mischenko S. P., “Tozhdestvo engelevosti i ego prilozheniya”, Matem. sb., 121 (163) (1983), 423–430 | Zbl

[2] Volichenko I. B., Issledovanie nekotorykh ekstremalnykh mnogoobrazii algebr Li, Dis. ... kand. fiz.-matem. nauk, IM AN BSSR, Minsk, 1982

[3] Klyachko A. A., “Elementy, Li v tenzornoi algebre”, Sib. matem. zh., 15:6 (1974), 1296–1306

[4] Drenski V. S., “Predstavlenie simmetricheskoi gruppy i mnogoobraziya lineinykh algebr”, Matem. sb., 115 (157) (1980), 98–114 | MR

[5] Latyshev V. N., “Teorema Regeva o tozhdestvakh tenzornogo proizvedeniya $PI$-algebr”, UMN, 27:4 (1972), 213–214 | MR | Zbl

[6] Bahturin Ju. A., Lectures on Lie algebras, Akademie–Verlag, Berlin, 1978 | MR | Zbl

[7] Shirshov A. I., “O nekotorykh neassotsiativnykh nil-koltsakh i algebraicheskikh algebrakh”, Matem. sb., 41 (83) (1957), 381–394 | Zbl

[8] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl