# Unipotent 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 for linear algebraic group

A **unipotent linear algebraic group** is a linear algebraic group in which every element is a unipotent element.

### Definition for affine algebraic group

A **unipotent affine algebraic group** is an affine algebraic group that becomes a unipotent linear algebraic group under the natural interpretation of the affine algebraic group as a linear algebraic group.

## Relation with group properties

In the finite-dimensional case, any unipotent algebraic group is a nilpotent group, and in the linear case, the order of matrices used (i.e., the dimension of the vector space being acted upon) is an upper bound on the nilpotency class (in fact, the nilpotency class must be strictly *less* than the order of matrices).