In mathematics a p-group is called power closed if for every section of the product of powers is again a th power. Regular p-groups are an example of power closed groups. On the other hand, powerful p-groups, for which the product of powers is again a 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 . References Group theory P-groups