Power closed

In mathematics a p-group formula_1 is called power closed if for every section formula_2 of formula_1 the product of formula_4 powers is again a formula_4th power.
Regular p-groups are an example of power closed groups. On the other hand, powerful p-groups, for which the product of formula_4 powers is again a formula_4th 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 .