Difference between revisions of "Any algebraic group has a unique closed normal linear algebraic subgroup so that the quotient group is an abelian variety"

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(Created page with "==Statement== Suppose <math>G</math> is an algebraic group over a field <math>K</math>. Then, there is a unique closed [[linear ...")
 
 
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==Statement==
 
==Statement==
  
Suppose <math>G</math> is an [[algebraic group]] over a field <math>K</math>. Then, there is a unique [[closed subgroup of an algebraic group|closed]] [[linear algebraic group|linear algebraic]] [[normal subgroup]] of <math>G</math> such that the [[quotient group]] <math>G/H</math> is an [[abelian variety]].
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Suppose <math>G</math> is a [[finite-dimensional algebraic group]] over a field <math>K</math>. Then, there is a unique [[closed subgroup of an algebraic group|closed]] [[linear algebraic group|linear algebraic]] [[normal subgroup]] of <math>G</math> such that the [[quotient group]] <math>G/H</math> is an [[abelian variety]].

Latest revision as of 17:25, 1 January 2012

Statement

Suppose G is a finite-dimensional algebraic group over a field K. Then, there is a unique closed linear algebraic normal subgroup of G such that the quotient group G/H is an abelian variety.