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.