Power closed

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