Subgroup with abnormal normalizer: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Abnormal subgroup]] | * [[Weaker than::Abnormal subgroup]] | ||
* [[Pronormal subgroup]] | * [[Weaker than::Pronormal subgroup]]: {{proofofstrictimplicationat|[[Normalizer of pronormal implies abnormal]]|[[Abnormal normalizer not implies pronormal]]}} | ||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Subgroup with weakly abnormal normalizer]] | * [[Stronger than::Subgroup with weakly abnormal normalizer]] | ||
Revision as of 21:58, 19 September 2008
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]
Definition
A subgroup with abnormal normalizer is a subgroup in a group whose normalizer is an abnormal subgroup.
Relation with other properties
Stronger properties
- Abnormal subgroup
- Pronormal subgroup: For proof of the implication, refer Normalizer of pronormal implies abnormal and for proof of its strictness (i.e. the reverse implication being false) refer Abnormal normalizer not implies pronormal.