Implementation Notes

The algorithms for recognizing Frobenius elements in Galois groups are described in [Dokchitser and Dokchitser, 2013]. They rely on the cycle type identification, Serre’s trick for alternating groups and the general machinery from [Dokchitser and Dokchitser, 2013]. Magma is usually able to handle Galois groups of size \(<10000\) acting on a small number of points easily, and much larger special groups such as \(A_n\) and \(S_n\).