Intermediately normal-to-characteristic subgroup
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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]
- Whenever it is normal in any intermediate subgroup, it is also characteristic in the intermediate subgroup.
- It is an intermediately characteristic subgroup in its normalizer.
Definition with symbols
- For any subgroup of containing such that is normal in , is characteristic in .
- is characteristic in any subgroup of contained in its normalizer .
In terms of the in-normalizer operator
This property is obtained by applying the in-normalizer operator to the property: intermediately characteristic subgroup
View other properties obtained by applying the in-normalizer operator
A subgroup is intermediately normal-to-characteristic in if and only if is an intermediately characteristic subgroup in .
Relation with other properties
- Intermediately automorph-conjugate subgroup
- Sylow subgroup
- Hall subgroup
- Join of intermediately automorph-conjugate subgroups
Intermediate subgroup condition
YES: This subgroup property satisfies the intermediate subgroup condition: if a subgroup has the property in the whole group, it has the property in every 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 SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition