Group having no proper nontrivial transitively normal subgroup

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Definition

A nontrivial group is termed a group having no proper nontrivial transitively normal subgroup if the only 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.

Formalisms

In terms of the simple group operator

This property is obtained by applying the simple group operator to the property: transitively normal subgroup
View other properties obtained by applying the simple group operator

Relation with other properties

Stronger properties

Weaker properties