Some unitary groups as Galois groups over \({\mathbb{Q}}\) (Q749616)

The author shows that some finite unitary and special unitary groups are realizable as Galois groups over \({\mathbb{Q}}\). His method is based on an idea of Feit which starts from a finite simple group G with a nontrivial outer automorphism \(\rho\) which can be extended to the universal central extension \(\tilde G\) such that the extended group \(\tilde G:\)\(<\rho >\) has trivial center. Then the rationality criteria can be applied to \(\tilde G:\)\(<\rho >\) to obtain (perhaps) a Galois realization for \(\tilde G:\)\(<\rho >\). Finally an easy descent argument leads to a Galois realization for \(\tilde G.\) In this manner the special unitary group \(\tilde G:\)\(=SU_ 3(p)\), \(p>2\), which has a nontrivial center of order 3 for \(p\equiv -1 mod 3\) is examined in the paper under review.