Abelian algebraic group

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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

Definition

An abelian algebraic group or commutative algebraic group is defined as an algebraic group that is also an abelian group (as an abstract group).

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
torus
split torus

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
nilpotent algebraic group
solvable algebraic group