EPIC sets in group theory
Solution 1:
The answer is given in the paper Abelian Forcing Sets, written by Joseph A. Gallian and Michael Reid. We have the following result:
Theorem: a set of integers $S$ is epic (called "abelian-forcing" in the paper) if and only if the gcd of the numbers $n(n-1)$ where $n$ runs over $S$ is equal to $2$.