A solution of the restricted Burnside problem for 2-groups
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 543-565 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A solution is given of the restricted Burnside problem for 2-groups.
@article{SM_1992_72_2_a15,
     author = {E. I. Zel'manov},
     title = {A~solution of the restricted {Burnside} problem for 2-groups},
     journal = {Sbornik. Mathematics},
     pages = {543--565},
     year = {1992},
     volume = {72},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1992_72_2_a15/}
}
TY  - JOUR
AU  - E. I. Zel'manov
TI  - A solution of the restricted Burnside problem for 2-groups
JO  - Sbornik. Mathematics
PY  - 1992
SP  - 543
EP  - 565
VL  - 72
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1992_72_2_a15/
LA  - en
ID  - SM_1992_72_2_a15
ER  - 
%0 Journal Article
%A E. I. Zel'manov
%T A solution of the restricted Burnside problem for 2-groups
%J Sbornik. Mathematics
%D 1992
%P 543-565
%V 72
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1992_72_2_a15/
%G en
%F SM_1992_72_2_a15
E. I. Zel'manov. A solution of the restricted Burnside problem for 2-groups. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 543-565. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a15/

[1] Burnside W., “On an unsettled question in the theory of discontinuous groups”, Quart. J. Pure Appl. Math., 33 (1902), 230–238 | Zbl

[2] Novikov P. S., Adyan S. I., “O beskonechnykh periodicheskikh gruppakh. I, II, III”, Izv. AN SSSR. Ser. matem., 32:1 (1968), 212–244 ; 2, 251–524 ; 3, 709–731 | Zbl

[3] Adyan S. I., Problema Bernsaida i tozhdestva v gruppakh, Nauka, M., 1975, s. 1–336 | MR | Zbl

[4] Lysenok I. G., “O probleme Bernsaida dlya nechetnykh pokazatelei $n\geqslant 115$”, Tez. soobsch. mezhdunar. konf. po algebre, Novosibirsk, 1989, 75

[5] Magnus W., “Uber Gruppen und zugeordnete Liesche Ringe”, J. reine angew. Math., 182 (1940), 142–149 | MR | Zbl

[6] Grun O., “Zusammenhang zwischen Potenzbildung und Kommutatorbildung”, J. reine angew. Math., 182 (1940), 158–177 | MR

[7] Zassenhaus H., “Ein Verfahren, jeder endlichen $p$-gruppe einem Lie-Ring mit der characteristik $p$ zu zuordnem”, Abh. Math. Sem. Univ. Hamburg, 13 (1940), 200–207 | DOI

[8] Baer R., “The higher commutator subgroups of a group”, Bull. Amer. Math. Soc., 50 (1944), 143–160 | DOI | MR | Zbl

[9] Magnus W. A., “A connection between the Baker - Hausdorff formula and a problem of Burnside”, Ann. Math., 52 (1950), 11–26 ; “Errata”, Ann. Math., 57 (1953), 606 | DOI | MR | DOI | MR | Zbl

[10] Hall P., Higman G., “On the $p$-length of $p$-soluble groups and reductions theorems for Burnside problem”, Proc. London Math. Soc., 6:3 (1956), 1–42 | DOI | MR | Zbl

[11] Kostrikin A. I., “O probleme Bernsaida”, Izv. AN SSSR. Ser. matem., 23:1 (1959), 3–34 | MR

[12] Kostrikin A. I., “Sendvichi v algebrakh Li”, Matem. sb., 110(152) (1979), 3–12 | MR | Zbl

[13] Kostrikin A. I., Vokrug Bernsaida, Nauka, M., 1986, s. 1–232 | MR

[14] Zelmanov E. I., “O nekotorykh problemakh teorii grupp i algebr Li”, Matem. sb., 180(222) (1989), 159–165

[15] Zelmanov E. I., “Reshenie oslablennoi problemy Bernsaida dlya grupp nechetnogo pokazatelya”, Izv. AN SSSR. Ser. matem., 54:1 (1990), 42–59 | MR | Zbl

[16] Zelmanov E. I., Kostrikin A. I., “Teorema o sendvichevykh algebrakh”, Tr. MMO, 183 (1988), 142–149

[17] Jacobson N., Structure and re 6 presentations of Jordan algebras, Amer. Math. Soc., Providence, R. I., 1969

[18] Jacobson N., “Lectures on quadratic Jordan algebras”, Tata Institute of Fundamental Research, 1969 | MR

[19] Zhevlakov K. A., Slinko A. M., Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978, s. 1–432 | MR | Zbl

[20] Bakhturin Yu. A., Tozhdestva v algebrakh Li, Nauka, M., 1984, s. 1–447 | MR

[21] Jordan P., von Neumann J., Wigner E., “On an algebraic generalization of the quantum mechanical formalism”, Ann. Math., 34:1 (1934), 29–64 | DOI

[22] McCrimmon K., “A general theory of Jordan rings”, Proc. Nat. Acad. Sci. USA, 55 (1966), 243–251 | DOI | MR

[23] McCrimmon K., Zelmanov E., “The structure of strongly prime quadratic Jordan algebras”, Adv. in Math., 69 (1988), 133–222 | DOI | MR | Zbl

[24] Meyberg K., “Jordan-Tripelsysteme und die Koecher-Konstruction von Lie-Algebren”, Math. Z., 115 (1970), 58–78 | DOI | MR | Zbl

[25] Meyberg K., Lectures on algebras and triple systems, Lect. Notes, Univ. Virginia, Charlottesville, 1972 | MR

[26] Loos O., Jordan Pairs, Springer-Verlag, New York, 1975 | MR | Zbl

[27] Thedy A., “$Z$-closed ideals in Jordan and alternative algebras”, Comm. in Algebra, 13 (1985), 2537–2566 | DOI | MR

[28] Martindale W. S., “Prime rings satisfying a generalized polynomial identity”, J. Algebra, 12:4 (1969), 576–584 | DOI | MR | Zbl

[29] Amitsur S. A., “Identities in rings with involutions”, Isr. J. Math., 7:1 (1969), 63–68 | DOI | MR | Zbl

[30] Markov V. T., “O razmernosti nekommutativnykh affinnykh algebr”, Izv. AN SSSR. Ser. matem., 37:2 (1973), 284–288 | Zbl

[31] Rowen L. H., “Some results on the center of a ring with polynomial identity”, Bull. Amer. Math. Soc., 79:1 (1973), 219–223 | DOI | MR | Zbl

[32] Kostrikin A. I., “O koltsakh Li, udovletvoryayuschikh usloviyu Engelya”, DAN SSSR, 108:4 (1956), 580–582 | MR | Zbl

[33] Plotkin B. I., “Ob algebraicheskikh mnozhestvakh elementov v gruppakh i algebrakh Li”, UMN, 13:6 (1958), 133–138 | MR | Zbl