Constructible group

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

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.