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We close a gap in the literature by showing that the full covering groups ofthe Mathieu group $M_{22}$ and of its automorphism group $Aut(M_{22})$ occur asthe Galois group of $\mathbb{Q}$-regular Galois extensions of $\mathbb{Q}(t)$.

Covering groups of $M_{22}$ as regular Galois groups over $\mathbb{Q}$