Simple algebraic group

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 group of a property encountered in group. Specifically, it is a algebraic group property analogous to the group property: simple group
View other analogues of simple group | View other analogues in algebraic groups of group properties (OR, View as a tabulated list)

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

• Semisimple algebraic group
• Reductive algebraic group