Some Lie rings associated with Burnside groups
Authors:
M. F. Newman and Michael Vaughan-Lee
Journal:
Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 1-3
MSC (1991):
Primary 17-04, 17B30, 20D15
DOI:
https://doi.org/10.1090/S1079-6762-98-00039-0
Published electronically:
February 13, 1998
MathSciNet review:
1600472
Full-text PDF Free Access
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Additional Information
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.
- George Havas, M. F. Newman, and M. R. Vaughan-Lee, A nilpotent quotient algorithm for graded Lie rings, J. Symbolic Comput. 9 (1990), no. 5-6, 653–664. Computational group theory, Part 1. MR 1075429, DOI https://doi.org/10.1016/S0747-7171%2808%2980080-6
- M. F. Newman and E. A. O’Brien, Application of computers to questions like those of Burnside. II, Internat. J. Algebra Comput. 6 (1996), no. 5, 593–605. MR 1419133, DOI https://doi.org/10.1142/S0218196796000337
- Michael Vaughan-Lee, The restricted Burnside problem, 2nd ed., London Mathematical Society Monographs. New Series, vol. 8, The Clarendon Press, Oxford University Press, New York, 1993. MR 1364414
- Michael Vaughan-Lee, The nilpotency class of finite groups of exponent $p$, Trans. Amer. Math. Soc. 346 (1994), no. 2, 617–640. MR 1264152, DOI https://doi.org/10.1090/S0002-9947-1994-1264152-8
- Michael Vaughan-Lee and E. I. Zel′manov, Upper bounds in the restricted Burnside problem, J. Algebra 162 (1993), no. 1, 107–145. MR 1250531, DOI https://doi.org/10.1006/jabr.1993.1245
- G. E. Wall, On the Lie ring of a group of prime exponent, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Springer, Berlin, 1974, pp. 667–690. Lecture Notes in Math., Vol. 372. MR 0357630
- G. E. Wall, On the Lie ring of a group of prime exponent. II, Bull. Austral. Math. Soc. 19 (1978), no. 1, 11–28. MR 522176, DOI https://doi.org/10.1017/S0004972700008406
- 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.
- 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.
- Michael Vaughan-Lee, The restricted Burnside problem, London Mathematical Society Monographs, New Series, vol. 8, 2nd ed., Clarendon Press, Oxford, 1993.
- Michael Vaughan-Lee, The nilpotency class of finite groups of exponent $p$, Trans. Amer. Math. Soc. 346 (1994), 617–640.
- Michael Vaughan-Lee and E. I. Zelmanov, Upper bounds in the restricted Burnside problem, J. Algebra 162 (1993), 107–145.
- 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.
- G. E. Wall, On the Lie ring of a group of prime exponent. II, Bull. Austral. Math. Soc. 19 (1978), 11–28.
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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
Received by editor(s):
November 20, 1997
Published electronically:
February 13, 1998
Communicated by:
Efim Zelmanov
Article copyright:
© Copyright 1998
American Mathematical Society
