Generating set in the powered sense for a powered group for a set of primes

Definition
Suppose $$\pi$$ is a set of prime numbers and $$G$$ is a $$\pi$$-powered group. A subset $$S$$ of $$G$$ is termed a generating set in the $$\pi$$-powered sense for $$G$$ if $$G$$ equals the $$\pi$$-powered subgroup generated by $$S$$ in $$G$$.