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

Abstract | References | Similar Articles | 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.

**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**

Retrieve articles in *Electronic Research Announcements of the American Mathematical Society*
with MSC (1991):
17-04,
17B30,
20D15

Retrieve articles in all journals with MSC (1991): 17-04, 17B30, 20D15

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:
https://doi.org/10.1090/S1079-6762-98-00039-0

Received by editor(s):
November 20, 1997

Published electronically:
February 13, 1998

Communicated by:
Efim Zelmanov

Article copyright:
© Copyright 1998
American Mathematical Society