Maximal Overgroups of Singer Elements in Classical Groups

In this paper, we use the results of a recent paper by Guralnick, Penttila, Praeger, and Saxl [Proc. London Math. Soc.78 (1999), 167–214] to calculate an explicit list of the maximal overgroups of the Singer elements in the finite special linear, general unitary, special unitary, symplectic, and minus type orthogonal groups.