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A problem in lie rings

Published online by Cambridge University Press:  18 May 2009

James Wiegold
James Wiegold
Affiliation:
University College, Cardiff, Wales
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An important step in the proof of Kostrikin's fundamental theorem [2] on finite groups of prime exponent is the following result.

Theorem 1. Let L be a Lie algebra of characteristic p satisfying the t-th Engel condition for some t<p, and suppose that L is generated by elements that are right-Engel of length 2. Then L is locally nilpotent.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 139 - 142
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Gruenberg, K. W., Two theorems on Engel groups, Proc. Cambridge Philos. Soc. 49 (1953), 377–380.CrossRefGoogle Scholar
2.Kostrikin, A. I., On Burnside's Problem, Izv. Akad. Nauk. SSSR. Ser. Mat. 23 (1959), 3–34.Google Scholar