Paranormal subgroup (original) (raw)
In mathematics, in the field of group theory, a paranormal subgroup is a subgroup such that the subgroup generated by it and any conjugate of it, is also generated by it and a conjugate of it within that subgroup. In symbols, is paranormal in if given any in , the subgroup generated by and is also equal to . Equivalently, a subgroup is paranormal if its weak closure and normal closure coincide in all intermediate subgroups. Here are some facts relating paranormality to other subgroup properties:
| Property | Value |
|---|---|
| dbo:abstract | In mathematics, in the field of group theory, a paranormal subgroup is a subgroup such that the subgroup generated by it and any conjugate of it, is also generated by it and a conjugate of it within that subgroup. In symbols, is paranormal in if given any in , the subgroup generated by and is also equal to . Equivalently, a subgroup is paranormal if its weak closure and normal closure coincide in all intermediate subgroups. Here are some facts relating paranormality to other subgroup properties: * Every pronormal subgroup, and hence, every normal subgroup and every abnormal subgroup, is paranormal. * Every paranormal subgroup is a polynormal subgroup. * In finite solvable groups, every polynormal subgroup is paranormal. (en) |
| dbo:wikiPageExternalLink | https://books.google.com/books%3Fid=iXXAZ3dmkNwC&dq=Paranormal+subgroup&pg=PA258 |
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| dbo:wikiPageWikiLink | dbr:Mathematics dbr:Normal_subgroup dbr:Generating_set_of_a_group dbr:Conjugacy_class dbr:Subgroup dbr:Polynormal_subgroup dbr:Abnormal_subgroup dbc:Subgroup_properties dbr:Group_theory dbr:Pronormal_subgroup |
| dbp:wikiPageUsesTemplate | dbt:Cite_book dbt:One_source |
| dct:subject | dbc:Subgroup_properties |
| rdf:type | yago:WikicatSubgroupProperties yago:Abstraction100002137 yago:Possession100032613 yago:Property113244109 yago:Relation100031921 |
| rdfs:comment | In mathematics, in the field of group theory, a paranormal subgroup is a subgroup such that the subgroup generated by it and any conjugate of it, is also generated by it and a conjugate of it within that subgroup. In symbols, is paranormal in if given any in , the subgroup generated by and is also equal to . Equivalently, a subgroup is paranormal if its weak closure and normal closure coincide in all intermediate subgroups. Here are some facts relating paranormality to other subgroup properties: (en) |
| rdfs:label | Paranormal subgroup (en) |
| owl:sameAs | freebase:Paranormal subgroup yago-res:Paranormal subgroup wikidata:Paranormal subgroup https://global.dbpedia.org/id/4tFQP |
| prov:wasDerivedFrom | wikipedia-en:Paranormal_subgroup?oldid=1123998820&ns=0 |
| foaf:isPrimaryTopicOf | wikipedia-en:Paranormal_subgroup |
| is dbo:wikiPageWikiLink of | dbr:Normal_subgroup dbr:Polynormal_subgroup dbr:Abnormal_subgroup dbr:Pronormal_subgroup |
| is foaf:primaryTopic of | wikipedia-en:Paranormal_subgroup |