AbstractThe maximal subgroups of the finite classical groups are divided by a theorem of Aschbacher into nine classes. In this paper, the authors show how to construct those maximal subgroups of the finite classical groups of linear, symplectic or unitary type that lie in the first eight of these classes. The ninth class consists roughly of absolutely irreducible groups that are almost simple modulo scalars, other than classical groups over the same field in their natural representation. All of these constructions can be carried out in low-degree polynomial time.
The maximal subgroups of the finite classical groups are divided into nine classes by Aschbacher's theorem. In this paper, we give explicit transcendental bases of the invariant subfields of those maximal subgroups of classical groups of linear, symplectic and unitary cases that lie in the first two of these classes. Also, we show that the invariant rings of the maximal subgroups of the finite linear groups that lie in the first class are polynomial rings.
Constructing Maximal Subgroups of Classical Groups
