Power closed

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In mathematics a p-group G is called power closed if for every section H of G the product of pk powers is again a pkth power.

Regular p-groups are an example of power closed groups. On the other hand powerful p-groups, for which the product of pk powers is again a pkth 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).

[edit] References

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Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (January 2008)
  • Mann, Avinoam (2005), “The number of generators of finite p-groups”, Journal of Group Theory 8 (3): 317–337, MR2137973, ISSN 1433-5883 


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