Paranormal subgroup
http://dbpedia.org/resource/Paranormal_subgroup an entity of type: WikicatSubgroupProperties
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:
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Paranormal subgroup
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3593691
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1123998820
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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.
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1351