Divisible group for a set of primes

Definition
Let $$\pi$$ be a set of primes. A group $$G$$ is termed $$\pi$$-divisible if it satisfies the following equivalent definitions:

Related notions

 * Powered group for a set of primes
 * Powering-injective group for a set of primes
 * Torsion-free group for a set of primes

Conjunction with group properties

 * Nilpotent group that is divisible for a set of primes is the conjunction with the property of being a nilpotent group.

Journal references

 * : This paper uses the notation $$E_{\pi}$$-group to describe what we call a $$\pi$$-divisible group. The notation is introduced in Section 2, Page 218 (second page of the paper).