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Some Lie rings associated with Burnside groups
Author(s):
M.
F.
Newman;
Michael
Vaughan-Lee
Journal:
Electron. Res. Announc. Amer. Math. Soc.
4
(1998),
1-3.
MSC (1991):
Primary 17-04, 17B30, 20D15
Posted:
February 13, 1998
MathSciNet review:
1600472
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Abstract:
We describe some calculations in graded Lie rings which provide a fairly sharp upper bound for the nilpotency class and for the order of the restricted Burnside group on two generators with exponent 7.
References:
- 1.
- George 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 92d:20054
- 2.
- M. F. Newman and E. A. O'Brien, Application of computers to questions like those of Burnside. II, Internat. J. Algebra Comput. 6 (1996), 593-605. MR 97k:20002
- 3.
- Michael Vaughan-Lee, The restricted Burnside problem, London Mathematical Society Monographs, New Series, vol. 8, 2nd ed., Clarendon Press, Oxford, 1993. MR 98b:20047
- 4.
- Michael Vaughan-Lee, The nilpotency class of finite groups of exponent
 , Trans. Amer. Math. Soc. 346 (1994), 617-640. MR 95g:20021 - 5.
- Michael Vaughan-Lee and E. I. Zelmanov, Upper bounds in the restricted Burnside problem, J. Algebra 162 (1993), 107-145. MR 94j:20019
- 6.
- G. E. Wall, On the Lie ring of a group of prime exponent, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973, pp. 667-690, Lecture Notes in Math., vol. 372, Springer-Verlag, Berlin, Heidelberg, New York, 1974. MR 50:10098
- 7.
- G. E. Wall, On the Lie ring of a group of prime exponent. II, Bull. Austral. Math. Soc. 19 (1978), 11-28. MR 80b:20052
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Additional Information:
M.
F.
Newman
Affiliation:
Australian National University
Email:
newman@maths.anu.edu.au
Michael
Vaughan-Lee
Affiliation:
University of Oxford
Email:
vlee@maths.oxford.ac.uk
DOI:
10.1090/S1079-6762-98-00039-0
PII:
S 1079-6762(98)00039-0
Received by editor(s):
November 20, 1997
Posted:
February 13, 1998
Communicated by:
Efim Zelmanov
Copyright of article:
Copyright
1998,
American Mathematical Society
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