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On the Lie-Kolchin-Mal'cev theorem

Published online by Cambridge University Press:  09 April 2009

B. A. F. Wehrfritz
Affiliation:
Queen Mary College London E1 4NS United Kingdom
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Abstract

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We discuss generalizations of the Lie-Kolchin-Mal'cev theorem. For example we show that if G is a soluble linear group of degree n, then G contains a triangularizable subgroup T whose index in G is bounded by function of n only and such that T is normalized by every automorphism of G normalizing G0, the Zariski connected component of G containing the identity. We also prove that in certain situations at least the index of G0 in G can be bounded in terms of the degree and the ground field.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1978

References

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