Invariants of the finite orthogonal groups in odd dimension and even characteristic

Abstract: We describe the ring of invariants for the finite orthogonal groups in odd dimension and even characteristic acting on the defining representation. We construct a minimal algebra generating set and describe the relations among the generators. This ring of invariants is shown to be a complete intersection and thus is Cohen-Macaulay. This extends the previous computation of Kropholler, Mohseni Rajaei, and Segal valid over the field of order 2.