Invariants of Finite Orthogonal Groups of Plus Type in Odd Characteristic

We describe the ring of invariants for the finite orthogonal group of plus type in odd characteristic acting on its defining representation. We also describe the invariants of its Sylow subgroup in the defining characteristic. In both cases we construct minimal algebra generating sets and describe the relations among the generators. Both rings of invariants are shown to be Complete Intersections and thus are Cohen-Macaulay. We expect the techniques we use will generalise to give a systematic computation for rings of invariants for all of the finite classical groups.