Monolithic group

Symbol-free definition
A group is said to be monolithic if it has a unique defining ingredient::minimal normal subgroup, and this is contained in every nontrivial defining ingredient::normal subgroup. This minimal normal subgroup is termed a monolith.

Stronger properties

 * Weaker than::Simple group

Weaker properties

 * Stronger than::Subdirectly irreducible group
 * Stronger than::Directly indecomposable group

Related properties

 * One-headed group