Difference between revisions of "Simple algebraic group"

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{{algebraic group property}}
 
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{{analogue in-of|algebraic group|group|simple group}}
 
==Definition==
 
==Definition==
  

Revision as of 08:40, 6 September 2007

This article defines a property that can be evaluated for an algebraic group. it is probably not a property that can directly be evaluated, or make sense, for an abstract group|View other properties of algebraic groups
ANALOGY: This is an analogue in algebraic groups of the group property:
View other analogues of simple group | View other analogues in algebraic groups of group properties

Definition

An algebraic group over a field is said to be simple if it does not contain any proper nontrivial normal connected closed subgroup.

Note that in abstract group-theoretic terms, this does not force the group to be a simple group. However, it does force the group to be a quasisimple group.

Relation with other properties

Weaker properties