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XV.—Bounds for the Indices of Nilpotent and Solvable Lie Algebras*

Published online by Cambridge University Press:  14 February 2012

E. M. Patterson
E. M. Patterson
Affiliation:
United College, University of St Andrews.
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Synopsis

By examining certain connections between the derivatives and the powers of a Lie algebra, bounds are obtained for the indices of nilpotent Lie algebras over an arbitrary field. The results are used to obtain bounds for the indices of solvable Lie algebras over a field of characteristic zero.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 64 , Issue 2 , 1954 , pp. 200 - 208
Copyright
Copyright © Royal Society of Edinburgh 1954

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References

References to Literature

Jacobson, N., 1935. “Rational methods in the theory of Lie algebras”, Ann. Math., 36, 875–881.Google Scholar
Magnus, W., 1937. “Über Beziehungen Zwischen höheien Kommutatoren”, J. reine angew Math., 177, 105–115.Google Scholar
Patterson, E. M., 1955. “Note on nilpotent and solvable algebras”, Proc. Camb. Phil. Soc., 51, 37–40.Google Scholar