Group in which every weakly abnormal subgroup is abnormal

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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 in which every weakly abnormal subgroup is abnormal is a group satisfying the condition that any weakly abnormal subgroup of it is an abnormal subgroup.

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 (weakly abnormal subgroup) satisfies the second property (abnormal subgroup), and vice versa.
View other group properties obtained in this way

Relation with other properties

Stronger properties