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Book Review
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Book Information
Author(s):
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(s):
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:
- [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.
- [2 ]
- S. I. Adyan and A. A. Razborov , Periodic groups and Lie algebras, Uspekhi Mat. Nauk \afterall (Russian) \textbf{42} (1987), 3--68.
- [3 ]
- S. I. Adyan and N. N. Repin , Lower bounds for the orders of maximal groups of prime exponent, Mat. Zametki\afterall (Russian) \textbf{44} (1988), 161--176.
- [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. \textbf{208} (1991), 401--409.
- [5 ]
- S. Bachmuth, H. Y. Mochizuki, and D. Walkup , A nonsolvable group of exponent \RM 5, Bull. Amer. Math. Soc. \textbf{76} (1970), 638--640.
- [6]
- W. Burnside, On an unsettled question in the theory of discontinuous groups, Quart. J. Pure Appl. Math. \textbf{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.
- [8]
- E. S. Golod, On nil-algebras and finitely approximable $p$-groups, Akad. Nauk SSSR Ser. Mat. \textbf{28} (1964), 273--276; English transl., Amer. Math. Soc. Transl. Ser. 2 {\bf 48} (1965), 103--106.
- [9 ]
- N. D. Gupta and M. F. Newman , The nilpotency class of finitely generated groups of exponent \RM 4, Lecture Notes in Math., vol. 372, Springer-Verlag, Berlin and New York, 1974, pp.~330--332.
- [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) \textbf{6} (1956), 1--42.
- [11 ]
- G. Havas, M. F. Newman and M. R. Vaughan-Lee , A nilpotent quotient algorithm for graded Lie rings, J. Symbolic Comput. \textbf{9} (1990), 653--664.
- [12]
- G. Higman, On finite groups of exponent \RM 5, Proc. Cambridge Philos. Soc. \textbf{52} (1956), 381--390.
- [13]
- A. I. Kostrikin, On Burnside's problem, Dokl. Akad. Nauk SSSR \afterall (Russian) \textbf{119} (1958), 1081--1084.
- [14]
- A. I. Kostrikin, On Burnside's problem, Izv. Akad. Nauk SSSR Ser. Math. \afterall (Russian) \textbf{23} (1959), 3--34.
- [15]
- A. I. Kostrikin, Sandwiches in Lie algebras, Mat. Sb. \afterall (Russian) \textbf{110} (1979), 3--12.
- [16 ]
- F. Levi and B. L. van der Waerden , \"Uber eine besondere Klasse von Gruppen, Abh. Math. Sem. Univ. Hamburg \textbf{9} (1933), 154--158.
- [17]
- W. Magnus, A connection between the Baker-Hausdorff formula and a problem of Burnside, Ann. of Math. \textbf{52} (1950), 111--126.
- [18]
- Yu. P. Razmyslov, On Engel Lie algebras, Algebra i Logika \afterall (Russian) \textbf{10} (1971), 33--44.
- [19]
- Yu. P. Razmyslov, On a problem of Hall and Higman, Izv. Akad. Nauk SSSR, Ser. Mat.\afterall (Russian) \textbf{42} (1978), 833--847.
- [20]
- M. R. Vaughan-Lee, Lie rings of groups of prime exponent, J. Austral. Math. Soc. Ser. A \textbf{49} (1990), 386--398.
- [21]
- E. I. Zel\cprime manov, Solution of the restricted Burnside problem for groups of odd exponent, Izv. Akad. Nauk SSSR, Ser. Mat.\afterall (Russian) \textbf{54} (1990), 42--59.
- [22]
- E. I. Zel\cprime manov, Solution of the restricted Burnside problem for \RM 2-groups, Mat. Sb.\afterall (Russian) \textbf{182} (1991), 568--592.
- [23 ]
- E. I. Zel\cprime manov and A. I. Kostrikin , A theorem on sandwich algebras, Trudy Mat. Inst. Steklov\afterall (Russian) \textbf{183} (1990), 106--111.
Additional Information:
Reviewer(s):
M. F.
Newman
Reviewer(s):
G. E.
Wall
Review Information:
Journal:
Bull. Amer. Math. Soc.
28
(1993),
157-161.
DOI:
10.1090/S0273-0979-1993-00341-0
PII:
S 0273-0979(1993)00341-0
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