**Journal of Lie Theory
**

Vol. 8, No. 2, pp. 211-217 (1998)

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Normalizers and centralizers of reductive subgroups of almost connected Lie groups

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D. Poguntke

Fakultät für Mathematik

Universität Bielefeld

Postfach 100 131

D-33501 Bielefeld

poguntke@mathematik.uni-bielefeld.de

**Abstract:** If ${\scriptstyle M}$ is an almost connected Lie subgroup of an almost connected Lie group ${\scriptstyle G}$ such that the adjoint group ${\scriptstyle M}$ is reductive then the product of ${\scriptstyle M}$ and its centralizer is of finite index in the normalizer. The method of proof also gives a different approach to the Weyl groups in the sense of [6].

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