Group of prime power order generated by two elementary abelian normal subgroups

Definition
A group of prime power order $$P$$ is said to be a group of prime power order generated by two elementary abelian normal subgroups if there are two elementary abelian normal subgroups $$E_1$$ and $$E_2$$ of $$P$$ such that $$P = E_1E_2$$.

Weaker properties

 * Stronger than::Group of nilpotency class two
 * Stronger than::Group of Frattini length two
 * Stronger than::Group of prime power order generated by elementary abelian normal subgroups
 * Stronger than::Group of prime power order generated by abelian normal subgroups