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A non-nilpotent Lie ring satisfying the Engel condition and a non-nilpotent Engel group

Published online by Cambridge University Press:  24 October 2008

P. M. Cohn
P. M. Cohn
Affiliation:
The UniversityManchester 13
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Extract

Let L be a Lie ring and denote the product of x and y in L by [x, y]. The ring L is said to satisfy the Engel condition (cf. (1)), if for every pair of elements x, yεL there is an integer k = k(x, y)such that

If k(x, y) can be taken equal to a fixed integer n for all x, y ε L then L is said to satisfy the n-th Engel condition.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 3 , July 1955 , pp. 401 - 405
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

(1)Gruenberg, K. W.Two theorems on Engel groups. Proc. Camb. phil. Soc. 49 (1953), 377–80.CrossRefGoogle Scholar
(2)Higgins, P. J.Lie rings satisfying the Engel condition. Proc. Camb. phil. Soc. 50 (1954), 8–15.CrossRefGoogle Scholar
(3)Zorn, M.On a theorem of Engel. Bull. Amer. math. Soc. 43 (1937), 401–4.CrossRefGoogle Scholar