Subgroup with abnormal normalizer: Difference between revisions
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{{subgroup property}} | {{subgroup property composition|normal subgroup|abnormal subgroup}} | ||
==Definition== | ==Definition== | ||
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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 than::Characteristic subgroup of pronormal subgroup]] | |||
===Weaker properties=== | ===Weaker properties=== | ||
* [[Subgroup with weakly abnormal normalizer]] | * [[Stronger than::Subgroup with weakly abnormal normalizer]] | ||
Latest revision as of 16:19, 11 February 2009
This page describes a subgroup property obtained as a composition of two fundamental subgroup properties: normal subgroup and abnormal subgroup
View other such compositions|View all subgroup properties
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.
- Characteristic subgroup of pronormal subgroup