Misplaced Pages

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Polynormal subgroup" – news · newspapers · books · scholar · JSTOR (November 2022) (Learn how and when to remove this message)

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 ${\displaystyle H}$ of a group ${\displaystyle G}$ is called polynormal if for any ${\displaystyle g\in G}$ the subgroup ${\displaystyle K=H^{<g>}}$ is the same as ${\displaystyle H^{H^{<g>}}}$.

Here are the relationships with other subgroup properties:

• Every weakly pronormal subgroup is polynormal.
• Every paranormal subgroup is polynormal.

References

1. "Polynormal subgroup - Groupprops". groupprops.subwiki.org. Retrieved 2023-08-22.

This group theory-related article is a stub. You can help Misplaced Pages by expanding it.

• v
• t
• e

• Subgroup properties
• Group theory stubs