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Polynomial Invariants of Certain Pseudo-Symplectic Groups Over Finite Fields of Characteristic Two

Let F q be a finite field of characteristic two, S be a nonsingular non-alternate symmetric matrix over F q and Ps n (F q , S) be the associated pseudo-symplectic group. Let Ps n (F q , S) act linearly on the polynomial ring F q [x 1,…, x n ]. In this note, we find an explicit set of generators of the ring of invariants of Ps n (F q , S) for n = 2, 4 and 2ν +1. In particular, the results assert that the ring of invariants of Ps 4(F q , S) is not a polynomial algebra but is an example of hypersurface and the ring of invariants of Ps 2ν+1(F q , S) is a complete intersection.