Power subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed a power subgroup if there exists an integer $$n$$ such that:

$$H = \{ g^n \mid g \in G \}$$

For a group of prime power order, the $$k^{th}$$ agemo subgroup are power subgroups if a product of $$(p^k)^{th}$$ powers is also a $$(p^k)^{th}$$ power.