Minimal group

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

This article is about a standard (though not very rudimentary) definition in an area related to, but not strictly part of, group theory

Definition

Symbol-free definition

A group (possibly with additional structures and relations) is said to be minimal if all its proper definable subgroups are finite.

Relation with other properties

Weaker properties

• Connected group for logicists
• Centralizer-finite group
• Centralizer-connected group