# Reductive 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

### Definition with symbols

A linear algebraic group over a field is said to be **reductive** if it satisfies the following equivalent conditions:

- It has no nontrivial normal unipotent connected closed subgroup.
- Its unipotent radical is the trivial subgroup.

## Relation with other properties

### Stronger properties

Stronger properties of algebraic groups include:

### Weaker properties

Weaker properties of algebraic groups include: