Aridity index: Difference between revisions
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In [[mathematics]], in the field of [[group theory]], a [[subgroup]] of a [[group (mathematics)|group]] is said to be '''polynormal''' if its [[conjugate closure|closure under conjugation]] by any element of the group can also be achieved via closure by conjugation by some element in the subgroup generated. | |||
In symbols, a subgroup <math>H</math> of a group <math>G</math> is called polynormal if for any <math>g \in G</math> the subgroup <math>K = H^{<g>}</math> is the same as <math>H^{H^{<g>}}</math>. | |||
Here are the relationships with other subgroup properties: | |||
* Every weakly [[pronormal subgroup]] is polynormal. | |||
* Every [[paranormal subgroup]] is polynormal. | |||
[[Category:Subgroup properties]] | |||
{{Abstract-algebra-stub}} | |||
Latest revision as of 10:02, 15 March 2013
In mathematics, in the field of group theory, a subgroup of a group is said to be polynormal if its closure under conjugation by any element of the group can also be achieved via closure by conjugation by some element in the subgroup generated.
In symbols, a subgroup of a group is called polynormal if for any the subgroup is the same as .
Here are the relationships with other subgroup properties:
- Every weakly pronormal subgroup is polynormal.
- Every paranormal subgroup is polynormal.