Subdirectly irreducible group

Symbol-free definition
A group is said to be subdirectly irreducible if:


 * Any expression of the group as subdirect product has that the projection map to at least one of the factors is an isomorphism
 * The trivial subgroup of the group cannot be expressed as an intersection of two nontrivial normal subgroups

Stronger properties

 * Weaker than::Simple group
 * Weaker than::Monolithic group

Weaker properties

 * Stronger than::Directly indecomposable group