Group in which every normal subgroup is characteristic

Definition

Symbol-free definition

A group is said to be a N=C-group if every normal subgroup of the group is characteristic.

Formalisms

In terms of the subgroup property collapse operator

This group property can be defined in terms of the collapse of two subgroup properties. In other words, a group satisfies this group property if and only if every subgroup of it satisfying the first property ({{{1}}}Property "Defining ingredient" (as page type) with input value "{{{1}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.) satisfies the second property ({{{2}}}Property "Defining ingredient" (as page type) with input value "{{{2}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.), and vice versa.
View other group properties obtained in this way

The property of being a N=C-group can be viewed as the following subgroup property collapse: characteristic subgroup = characteristic subgroup

Relation with other properties

Stronger properties

• N=FC-group
• Simple group
• Cyclic group

Weaker properties

• T-group: Here, normality is transitive
• N=PC-group: Here, every normal subgroup is potentially characteristic
• TN=C-group: Here, the characteristic subgroups are precisely the same as the transitively normal subgroups