Definably simple group

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

This is a variation of simplicity|Find other variations of simplicity | Read a survey article on varying simplicity

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 definably simple if it has no proper nontrivial definable normal subgroup.

Relation with other properties

Weaker properties

For infinite groups, the following properties are weaker: