Group having no proper nontrivial transitively normal subgroup

Definition
A nontrivial group is termed a group having no proper nontrivial transitively normal subgroup if the only defining ingredient::transitively normal subgroups of the group are the whole group and the trivial subgroup. Here, a subgroup is transitively normal if every normal subgroup of the subgroup is normal in the whole group.

Stronger properties

 * Weaker than::Simple group:

Weaker properties

 * Stronger than::Centrally indecomposable group
 * Stronger than::Directly indecomposable group
 * Centerless group unless the group is a simple Abelian group, i.e., a cyclic group of prime order.