Group in which every normal subgroup is characteristic

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Symbol-free definition

A group in which every normal subgroup is characteristic is a group such that every normal subgroup of the group is characteristic in the group.

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 can be viewed as the following subgroup property collapse: normal subgroup = characteristic subgroup

Relation with other properties

Stronger properties

• Group in which every normal subgroup is fully characteristic
• Simple group
• Cyclic group

Weaker properties

• Group in which every normal subgroup is potentially characteristic: Here, every normal subgroup is potentially characteristic
• T-group