Inverse Galois problem

Statement
The inverse Galois problem is the problem of finding all Galois-realizable groups over $$\mathbb{Q}$$.

Associated conjecture
It is believed that the property of being Galois-realizable over $$\mathbb{Q}$$ is the tautology for finite groups. In other words, it is believed that every finite group can be realized as the Galois group of some Galois extension over $$\mathbb{Q}$$.

Thus, the inverse Galois problem is sometimes thought of as the problem of determining whether or not every finite group can be expressed as the Galois group of some Galois extension (rather than the more general problem of understanding precisely what it means for a group to be Galois-realizable).