Absolutely regular p-group

Definition
A p-group $$G$$ is termed an absolutely regular p-group if $$|G/\mho^1(G)| \le p^{p-1}$$, where $$\mho^1(G)$$ denotes the first agemo subgroup of $$G$$, i.e., the subgroup of $$G$$ generated by $$g^p, g \in G$$.

Stronger properties

 * Weaker than::Group of prime order
 * Weaker than::Cyclic group of prime power order

Weaker properties

 * Stronger than::Regular p-group: