Abstract

Abstract:

A century ago, Camille Jordan proved that the complex general linear group ${\rm GL}_n(\Bbb{C})$ has the Jordan property: there is a Jordan constant ${\rm C}_n$ such that every finite subgroup $H\le{\rm GL}_n(\Bbb{C})$ has an abelian subgroup $H_1$ of index $[H:H_1]\le{\rm C}_n$. We show that every connected algebraic group $G$ (which is not necessarily linear) has the Jordan property with the Jordan constant depending only on $\dim G$, and that the full automorphism group ${\rm Aut}(X)$ of every projective variety $X$ has the Jordan property.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1133-1145
Launched on MUSE
2018-07-07
Open Access
No
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