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On the Lie-Kolchin-Mal'cev theorem

Part of: Other groups of matrices

Published online by Cambridge University Press:  09 April 2009

B. A. F. Wehrfritz
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

Secondary: 20H20: Other matrix groups over fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 3 , November 1978 , pp. 270 - 276
Copyright
Copyright © Australian Mathematical Society 1978

References

Borel, A. (1969), Linear Algebraic Groups (Benjamin, New York).Google Scholar
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Wehrfritz, B. A. F. (1978), “Nilpotence in groups of semilinear maps I”, Proc. London Math. Soc. (3) 36, 448–479.CrossRefGoogle Scholar