Realization of sporadic simple groups as Galois groups over cyclotomic fields.
The authors prove as a consequence of their Satz 1 the following interesting theorems. 1. The following 18 sporadic simple groups \(M_{11}\), \(M_{12}\), \(M_{22}\), \(J_ 1\), \(J_ 2\), \(HS\), \(Sz\), \(ON\), \(Co_ 3\), \(Co_ 2\), \(Co_ 1\), \(Fi_{22}\), \(Fi_{23}\), \(Fi'_{24}\), \(F_ 5\), \(F_ 3\), \(F_ 2\), \(F_ 1\) are realizable as Galois groups over the rational number field \({\mathbb Q}.\) 2. Let \({\mathbb Q}^{ab}={\mathbb Q}\) (all \(n\)th roots of unity for all \(n\)). Then all sporadic simple groups (except perhaps \(J_ 4)\) are realizable as Galois groups over \({\mathbb Q}^{ab}\).
sporadic simple groups as Galois groups over \({\mathbb Q}\)
scientific article; zbMATH DE number 3963968
scientific article