JORDAN PROPERTY FOR NON-LINEAR ALGEBRAIC GROUPS AND PROJECTIVE VARIETIES

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.