Realization of the Mathieu group M23 as a Galois group over Q

Determine whether there exists a Galois extension of the rational numbers Q whose Galois group is isomorphic to the Mathieu group M23.

Background

The paper reviews the status of the Inverse Galois Problem, which asks whether every finite group occurs as the Galois group of a field extension over Q. Many families of groups are known to be realizable, including symmetric and alternating groups, abelian and solvable groups, and numerous sporadic simple groups (e.g., several Mathieu groups and the Monster).

Despite these successes, the authors note that realizability remains unknown for certain specific groups. In particular, they highlight the Mathieu group M23 as a case where it is still unknown whether it can be realized as a Galois group over Q.