# Monolithic group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

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

## Contents

## Definition

### Symbol-free definition

A group is said to be **monolithic** if it has a unique minimal normal subgroup, and this is contained in *every* nontrivial normal subgroup. This minimal normal subgroup is termed a **monolith**.