Group in which every normal subgroup is fully invariant
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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
Definition
Symbol-free definition
A group is said to be a N=FC-group if every normal subgroup of the group is fully 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=FC-group can be expressed as the collapse of the following subgroup properties: normal subgroup = fully characteristic subgroup