dbo:abstract
|
- In mathematics, especially in the field of group theory, a pronormal subgroup is a subgroup that is embedded in a nice way. Pronormality is a simultaneous generalization of both normal subgroups and abnormal subgroups such as Sylow subgroups, . A subgroup is pronormal if each of its conjugates is conjugate to it already in the subgroup generated by it and its conjugate. That is, H is pronormal in G if for every g in G, there is some k in the subgroup generated by H and Hg such that Hk = Hg. (Here Hg denotes the conjugate subgroup gHg-1.) Here are some relations with other subgroup properties:
* Every normal subgroup is pronormal.
* Every Sylow subgroup is pronormal.
* Every pronormal subnormal subgroup is normal.
* Every abnormal subgroup is pronormal.
* Every pronormal subgroup is , that is, it has the .
* Every pronormal subgroup is paranormal, and hence polynormal. (en)
|
dbo:wikiPageExternalLink
| |
dbo:wikiPageID
| |
dbo:wikiPageLength
|
- 1736 (xsd:nonNegativeInteger)
|
dbo:wikiPageRevisionID
| |
dbo:wikiPageWikiLink
| |
dbp:wikiPageUsesTemplate
| |
dcterms:subject
| |
gold:hypernym
| |
rdf:type
| |
rdfs:comment
|
- In mathematics, especially in the field of group theory, a pronormal subgroup is a subgroup that is embedded in a nice way. Pronormality is a simultaneous generalization of both normal subgroups and abnormal subgroups such as Sylow subgroups, . A subgroup is pronormal if each of its conjugates is conjugate to it already in the subgroup generated by it and its conjugate. That is, H is pronormal in G if for every g in G, there is some k in the subgroup generated by H and Hg such that Hk = Hg. (Here Hg denotes the conjugate subgroup gHg-1.) (en)
|
rdfs:label
| |
owl:sameAs
| |
prov:wasDerivedFrom
| |
foaf:isPrimaryTopicOf
| |
is dbo:wikiPageWikiLink
of | |
is foaf:primaryTopic
of | |