Subnormal-to-normal subgroup

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]

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Definition

Symbol-free definition

A subgroup of a group is termed subnormal-to-normal if it is either normal in the whole group, or not subnormal in the whole group.

Every subgroup is subnormal-to-normal iff the group is a T-group.

Relation with other properties

Stronger properties

• Intermediately subnormal-to-normal subgroup
• Pronormal subgroup
• Weakly pronormal subgroup
• Contranormal subgroup
• Abnormal subgroup
• Weakly abnormal subgroup
• Paranormal subgroup
• Polynormal subgroup

Metaproperties

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