Covering groups of almost simple groups as Galois groups over \(\mathbb{Q}^{ab}(t)\) (Q677422)

The paper is a continuation of the article by \textit{J. Sonn} [J. Number Theory 47, No. 3, 398-404 (1994; Zbl 0805.12002)], where a criterion for solving central embedding problems over \(\mathbb Q^{ab}(t)\) is given (\(\mathbb Q^{ab}\) being the maximal abelian extension of \(\mathbb Q\)). The authors first give a purely group-theoretical version of such a criterion. Then, finding some stronger results than those proved by \textit{G. Malle, J. Saxl} and \textit{T. Weigel} [Geom. Dedicata 49, No. 1, 85-116 (1994; Zbl 0832.20029)], the unitary groups and the odd-dimensional orthogonal groups are regularly realized over \(\mathbb Q^{ab}(t)\) by rigidity methods. Finally, applying the criterion, any covering group of the above groups, as well as of some exceptional groups of Lie type and of the sporadic groups (except \(M_{22}\)), is regularly realized over \(\mathbb Q^{ab}(t)\). Hence, also by the results from the first mentioned paper, the central embedding problem over \(\mathbb Q^{ab}(t)\) is solved for most of the finite classical groups, with the main exception of the even-dimensional orthogonal groups.