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- Pronormal_subgroup 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, (Doerk & Hawkes 1992, I.§6).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 weakly pronormal, that is, it has the Frattini propertyEvery pronormal subgroup is paranormal, and hence polynormal".
- Pronormal_subgroup wikiPageID "3593621".
- Pronormal_subgroup wikiPageRevisionID "515126702".
- Pronormal_subgroup hasPhotoCollection Pronormal_subgroup.
- Pronormal_subgroup subject Category:Subgroup_properties.
- Pronormal_subgroup type Abstraction100002137.
- Pronormal_subgroup type Possession100032613.
- Pronormal_subgroup type Property113244109.
- Pronormal_subgroup type Relation100031921.
- Pronormal_subgroup type SubgroupProperties.
- Pronormal_subgroup 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, (Doerk & Hawkes 1992, I.§6).A subgroup is pronormal if each of its conjugates is conjugate to it already in the subgroup generated by it and its conjugate.".
- Pronormal_subgroup label "Pronormal subgroup".
- Pronormal_subgroup sameAs m.09nmvk.
- Pronormal_subgroup sameAs Q7249944.
- Pronormal_subgroup sameAs Q7249944.
- Pronormal_subgroup sameAs Pronormal_subgroup.
- Pronormal_subgroup wasDerivedFrom Pronormal_subgroup?oldid=515126702.
- Pronormal_subgroup isPrimaryTopicOf Pronormal_subgroup.