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Literature Cited
W. Magnus, “Über Gruppen and zugeordnete Liesche Ringe,” J. Reine Angew. Math.,182, 142–149 (1940).
O. Grun, “Zusammenhang zwischen Potenzbildung und Kommutatorbildung,” J. Reine Angew. Math.,182, 158–177 (1940).
H. Zassenhaus, “Ein Verfahren, jeder endlichen p-Gruppe einem Lie-Ring mit der Charakteristik p zu zuordnen,” Abh. Math. Sem. Univ. Hamburg,13, 200–207 (1940).
R. Baer, “The higher commutator subgroups of a group,” Bull. Am. Math. Soc.,50, 143–160 (1944).
W. Magnus, “A connection between the Baker-Hausdorff formula and a problem of Burnside,” Ann. Math.,52, 11–26 (1950).
P. S. Novikov and S. I. Adyan, “Infinite periodic groups. I, II, III,” Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 1, 212–244; No. 2, 251–524; No. 3, 709–731 (1968).
S. I. Adyan, The Problem of Burnside and Identities in Groups [in Russian], Nauka, Moscow (1975).
P. Hall and G. Higman, “On the p-length of p-soluble groups and reduction theorems for Burnside's problem,” Proc. London Math. Soc.,6, No. 3, 1–42 (1956).
I. N. Sanov, “A certain system of relations in periodic groups with a period-degree of a prime number,” Izv. Akad. Nauk SSSR, Ser. Mat.,15, 477–502 (1951).
M. Lazard, “Sur les groupes nilpotents et les anneaux de Lie,” Ann. Sci. École Norm. Sup.,71, No. 3, 101–190 (1954).
A. I. Kostrikin, “A problem of Burnside,” Izv. Akad. Nauk SSSR, Ser. Mat.,23, No. 1, 3–34 (1959).
A. I. Kostrikin, “Sandwiches in Lie algebras,” Mat. Sb.,110, 3–12 (1979).
A. I. Kostrikin, About Burnside [in Russian], Nauka, Moscow (1986).
F. J. Grunewald, G. Havas, J. L. Mennicke, and M. F. Newman, “Groups of exponent eight,” Bull. Austral. Math. Soc.,20, 7–16 (1979).
G. Higman, “Lie ring methods in the theory of finite nilpotent groups,” Proc. Int. Congr. Math., Edinburgh, 307–312 (1958).
E. I. Zel'manov, “On the nilpotency of nil algebras,” Lect. Notes Math., No. 1352, 227–240 (1986).
A. G. Kurosh, “Problems of ring theory connected with the Burnside problem on periodic groups, Izv. Akad. Nauk SSSR, Ser. Mat., No. 5, 233–240 (1941).
I. Kaplansky, “On a problem of Kurosh and Jacobson,” Bull. Am. Math. Soc.,52, No. 6, 496–500 (1946).
J. Levitzki, “On the radical of a general ring,” Bull. Am. Math. Soc.,49, 462–466 (1943).
A. I. Shirshov, “Rings with identity relations,” Mat. Sb.,43, 277–283 (1957).
E. I. Zel'manov, “Some problems of group theory and Lie algebras,” Mat. Sb.,180, No. 2, 1–8 (1989).
E. I. Zel'manov and A. I. Kostrikin, “A theorem on sandwich algebras,” Trudy Mat. Inst. V. A. Steklov Akad. Nauk SSSR, No. 183, 142–149 (1988).
A. I. Kostrikin, “Lie rings satisfying the Engel condition,” Dokl. Akad. Nauk SSSR,108, No. 4, 580–582 (1956).
B. L. Plotkin, “Algebraic sets of elements in groups and Lie algebras,” Usp. Mat. Nauk,13, No. 6, 133–138 (1958).
Yu. A. Bakhturin, Identities in Lie Algebras [in Russian], Nauka, Moscow (1985).
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Dedicated to the memory of A. I. Mal'tsev.
This paper, by way of an exception, is published without complete proofs.
Novosibirsk City. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 6, pp. 68–74, November–December, 1989.
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Zel'manov, E.I. Weakened Burnside problem. Sib Math J 30, 885–891 (1989). https://doi.org/10.1007/BF00970910
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DOI: https://doi.org/10.1007/BF00970910