Subgroup with self-normalizing normalizer

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]


Symbol-free definition

A subgroup of a group is termed a subgroup with self-normalizing normalizer if its normalizer in the whole group is a self-normalizing subgroup of the whole group.

Relation with other properties

Stronger properties

Opposite properties

A subgroup can have a self-normalizing normalizer and satisfy one of the properties below only if it is normal.

Incomparable properties


Intermediate subgroup condition

NO: This subgroup property does not satisfy the intermediate subgroup condition: it is possible to have a subgroup satisfying the property in the whole group but not satisfying the property in some intermediate subgroup.
ABOUT THIS PROPERTY: View variations of this property satisfying intermediate subgroup condition | View variations of this property not satisfying intermediate subgroup condition
ABOUT INTERMEDIATE SUBGROUP CONDITION: View other subgroup properties not satisfying intermediate subgroup condition| View facts about intermediate subgroup condition

Effect of property operators

The intermediately operator

Applying the intermediately operator to this property gives: intermediately subnormal-to-normal subgroup