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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
Affiliation:
The UniversityManchester 13
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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
Copyright
Copyright © Cambridge Philosophical Society 1955

References

REFERENCES

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(2)Higgins, P. J.Lie rings satisfying the Engel condition. Proc. Camb. phil. Soc. 50 (1954), 815.CrossRefGoogle Scholar
(3)Zorn, M.On a theorem of Engel. Bull. Amer. math. Soc. 43 (1937), 401–4.CrossRefGoogle Scholar