Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: A.\ I.\ Kostrikin
Title: Around Burnside
Additional book information: Ergeb. Math. Grenzgeb. (3), vol. 20, Springer-Verlag, New York, Berlin, and Heidelberg, 1990, 220 pp., US$82.00. ISBN 0-387-50602-0.

Author: Michael Vaughan-Lee
Title: The restricted Burnside problem
Additional book information: London Math. Soc. Monographs (N.S.), vol. 5, Oxford University Press, Oxford, 1990, 209 pp., US$57.50, ISBN 0-19-853573-2.

References [Enhancements On Off] (What's this?)

  • [1] S. I. Adyan, The Burnside problem and identities in groups, Izdat. "Nauka", Moscow, 1975; English transl., Ergebnisse der Math. Bd. 95, Springer-Verlag, Berlin, 1979. MR 0432770 (55:5753)
  • [2] S. I. Adyan and A. A. Razborov, Periodic groups and Lie algebras, Uspekhi Mat. Nauk 42 (1987), 3-68. (Russian) MR 898621 (89i:20033)
  • [3] S. I. Adyan and N. N. Repin, Lower bounds for the orders of maximal groups of prime exponent, Mat. Zametki 44 (1988), 161-176. (Russian) MR 969265 (90f:20054)
  • [4] M. Aschbacher, P. B. Kleidman, and M. W. Liebeck, Exponents of almost simple groups and an application to the restricted Burnside problem, Math. Z. 208 (1991), 401-409. MR 1134585 (92k:20058)
  • [5] S. Bachmuth, H. Y. Mochizuki, and D. Walkup, A nonsolvable group of exponent 5, Bull. Amer. Math. Soc. 76 (1970), 638-640. MR 0257209 (41:1862)
  • [6] W. Burnside, On an unsettled question in the theory of discontinuous groups, Quart. J. Pure Appl. Math. 33 (1902), 230-238.
  • [7] B. Chandler and W. Magnus, The history of combinatorial group theory: a case study in the history of ideas, Springer-Verlag, New York, 1982. MR 680777 (85c:01001)
  • [8] E. S. Golod, On nil-algebras and finitely approximable p-groups, Akad. Nauk SSSR Ser. Mat. 28 (1964), 273-276; English transl., Amer. Math. Soc. Transl. Ser. 2 48 (1965), 103-106. MR 0161878 (28:5082)
  • [9] N. D. Gupta and M. F. Newman, The nilpotency class of finitely generated groups of exponent 4, Lecture Notes in Math., vol. 372, Springer-Verlag, Berlin and New York, 1974, pp. 330-332. MR 0352265 (50:4752)
  • [10] P. Hall and G. Higman, On the p-length of p-soluble groups and reduction theorems for Burnside's problem, Proc. London Math. Soc. (3) 6 (1956), 1-42. MR 0072872 (17:344b)
  • [11] G. Havas, M. F. Newman and M. R. Vaughan-Lee, A nilpotent quotient algorithm for graded Lie rings, J. Symbolic Comput. 9 (1990), 653-664. MR 1075429 (92d:20054)
  • [12] G. Higman, On finite groups of exponent 5, Proc. Cambridge Philos. Soc. 52 (1956), 381-390. MR 0081285 (18:377e)
  • [13] A. I. Kostrikin, On Burnside's problem, Dokl. Akad. Nauk SSSR 119 (1958), 1081-1084. (Russian) MR 0132101 (24:A1948)
  • [14] -, On Burnside's problem, Izv. Akad. Nauk SSSR Ser. Math. 23 (1959), 3-34. (Russian) MR 0132100 (24:A1947)
  • [15] -, Sandwiches in Lie algebras, Mat. Sb. 110 (1979), 3-12. (Russian) MR 548513 (81e:17004)
  • [16] F. Levi and B. L. van der Waerden, Über eine besondere Klasse von Gruppen, Abh. Math. Sem. Univ. Hamburg 9 (1933), 154-158.
  • [17] W. Magnus, A connection between the Baker-Hausdorff formula and a problem of Burnside, Ann. of Math. 52 (1950), 111-126; Errata, Ann. of Math. 57 (1953), 606. MR 0038964 (12:476c)
  • [18] Yu. P. Razmyslov, On Engel Lie algebras, Algebra i Logika 10 (1971), 33-44. (Russian) MR 0294428 (45:3498)
  • [19] -, On a problem of Hall and Higman, Izv. Akad. Nauk SSSR, Ser. Mat. 42 (1978), 833-847. (Russian) MR 508829 (80d:20040)
  • [20] M. R. Vaughan-Lee, Lie rings of groups of prime exponent, J. Austral. Math. Soc. Ser. A 49 (1990), 386-398. MR 1074510 (91m:20059)
  • [21] E. I. Zel'manov, Solution of the restricted Burnside problem for groups of odd exponent, Izv. Akad. Nauk SSSR, Ser. Mat. 54 (1990), 42-59. (Russian) MR 1044047 (91i:20037)
  • [22] -, Solution of the restricted Burnside problem for 2-groups, Mat. Sb. 182 (1991), 568-592. (Russian) MR 1119009 (93a:20063)
  • [23] E. I. Zel'manov and A. I. Kostrikin, A theorem on sandwich algebras, Trudy Mat. Inst. Steklov 183 (1990), 106-111. (Russian) MR 1092020 (92h:17007)

Review Information:

Reviewer: M. F. Newman
Reviewer: G. E. Wall
Journal: Bull. Amer. Math. Soc. 28 (1993), 157-161
DOI: https://doi.org/10.1090/S0273-0979-1993-00341-0
American Mathematical Society