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2-hypernormalized subgroup
From Groupprops
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof.
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Contents |
Definition
Symbol-free definition
A subgroup of a group is termed 2-hypernormalized if its normalizer is a normal subgroup.
Relation with other properties
Stronger properties
Weaker properties
- Finitarily hypernormalized subgroup
- 2-subnormal subgroup: Also related:
Metaproperties
Transitivity
NO: This subgroup property is not transitive: a subgroup with this property in a subgroup with this property, need not have the property in the whole group
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ABOUT TRANSITIVITY: View a complete list of subgroup properties that are not transitive| View facts related to transitivity of subgroup properties | View a survey article on disproving transitivity
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.
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ABOUT INTERMEDIATE SUBROUP CONDITION: View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition
Transfer condition
This subgroup property does not satisfy the transfer condition
Facts about 2-hypernormalized subgroupRDF feed