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 properties
VIEW 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

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.

Relation with other properties

Stronger properties

• Simple group

Weaker properties

• Subdirectly irreducible group
• Directly indecomposable group

Related properties

• One-headed group