# Abelian algebraic group

From Groupprops

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

## Contents

## 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 |