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Finiteness conditions in soluble groups and Lie algebras

Published online by Cambridge University Press:  17 April 2009

Ian N. Stewart
Ian N. Stewart
Affiliation:
Mathematics Institute, University of Warwick, Coventry, England.
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Abstract

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We prove some new theorems and reprove some old ones about finitely generated soluble groups and Lie algebras by a uniform method. Among the applications are Gruenberg's Theorem on Engel groups, for which we obtain a very short proof; and the Milnor and Wolf polynomial growth theorem. It is shown that a finitely generated soluble group with all 2-generator subgroups polycyclic is itself polycyclic, and that a finitely generated soluble Lie algebra, all of whose inner derivations are algebraic, is finite-dimensional. This last result enables us to give a partial answer to a question of Jacobson.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 1 , August 1973 , pp. 43 - 48
Copyright
Copyright © Australian Mathematical Society 1973

References

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