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On the Associated Lie Ring and the Adjoint Group of a Radical Ring

Published online by Cambridge University Press:  20 November 2018

Hartmut Laue
Hartmut Laue*
Affiliation:
Mathematisches Seminar Der UniversitätOlshausenstr. 40 D 2300 Kiel 1 Bundesrepublik, Deutschland
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Abstract

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We investigate connections between the associated Lie ring and the adjoint group of a radical ring, studying their upper central chains. Part of a conjecture of S. A. Jennings is proved, and one of our results improves a theorem of his.

Keywords

16A22
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 2 , 01 June 1984 , pp. 215 - 222
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Jacobson, N., Lie Algebras, Wiley, New York-London 1962.Google Scholar
2. Jennings, S. A., The group ring of a class of infinite nilpotent groups, Canad. J. Math. 7 (1955), 169–187.Google Scholar
3. Jennings, S. A., Radical rings with nilpotent associated groups, Trans. Roy. Soc. Can. 49 ser. Ill (1955), 31–38.Google Scholar
4. Kaloujnine, L., Über gewisse Beziehungen zwischen einer Gruppe und ihren Automorphismen, Ber. math. Tagung Berlin 1953.Google Scholar