Jordan property for non-linear algebraic groups and projective varieties

Sheng Meng; De Qi Zhang

doi:10.1353/ajm.2018.0026

Jordan property for non-linear algebraic groups and projective varieties

Sheng Meng
, De Qi Zhang

National University of Singapore

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

A century ago, Camille Jordan proved that the complex general linear group GL_n(ℂ) has the Jordan property: there is a Jordan constant C_n such that every finite subgroup H ≤ GL_n(ℂ) has an abelian subgroup H₁ of index [H: H₁] ≤ 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 Aut(X) of every projective variety X has the Jordan property.

Original language	English
Pages (from-to)	1133-1145
Number of pages	13
Journal	American Journal of Mathematics
Volume	140
Issue number	4
DOIs	https://doi.org/10.1353/ajm.2018.0026
State	Published - Aug 2018
Externally published	Yes

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10.1353/ajm.2018.0026

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abstract = "A century ago, Camille Jordan proved that the complex general linear group GLn(ℂ) has the Jordan property: there is a Jordan constant Cn such that every finite subgroup H ≤ GLn(ℂ) has an abelian subgroup H1 of index [H: H1] ≤ Cn. 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 Aut(X) of every projective variety X has the Jordan property.",

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AB - A century ago, Camille Jordan proved that the complex general linear group GLn(ℂ) has the Jordan property: there is a Jordan constant Cn such that every finite subgroup H ≤ GLn(ℂ) has an abelian subgroup H1 of index [H: H1] ≤ Cn. 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 Aut(X) of every projective variety X has the Jordan property.

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Jordan property for non-linear algebraic groups and projective varieties

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