In mathematics a p-group ${\displaystyle G}$ is called power closed if for every section ${\displaystyle H}$ of ${\displaystyle G}$ the product of ${\displaystyle p^{k}}$ powers is again a ${\displaystyle p^{k}}$th power.

Regular p-groups are an example of power closed groups. On the other hand, powerful p-groups, for which the product of ${\displaystyle p^{k}}$ powers is again a ${\displaystyle p^{k}}$th power are not power closed, as this property does not hold for all sections of powerful p-groups.

The power closed 2-groups of exponent at least eight are described in ( Mann 2005, Th. 16).

References

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:  "Power closed" –  news · newspapers · books · scholar · JSTOR (January 2008) ( Learn how and when to remove this message)

• Mann, Avinoam (2005), "The number of generators of finite p-groups", Journal of Group Theory, 8 (3): 317–337, doi: 10.1515/jgth.2005.8.3.317, ISSN  1433-5883, MR  2137973, S2CID  122133846

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

• v
• t
• e