Abelian 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
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 |