This article defines a property of a group (possibly with additional operations and structure) as viewed in logic/model theory
A group (possibly with additional structures and relations) is said to be constructible if it is definable in a pure algebraically closed field.
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