# Constructible group

From Groupprops

*This article defines a property of a group (possibly with additional operations and structure) as viewed in logic/model theory*

## Contents

## Definition

### Symbol-free definition

A group (possibly with additional structures and relations) is said to be **constructible** if it is definable in a pure algebraically closed field.

## Facts

### Definable isomorphism to algebraic groups

`Further information: Weil-Hrushobski theorem`

Every constructible group is definable isomorphic to an algebraic group.

### Inner automorphism group

`Further information: Maxwell-Rosenlicht theorem`

The inner automorphism group of a constructible group is definably isomrohpic to a linear algebraic group.