Certain finite groups as automorphism groups of forms of higher degree

In this paper we shall be interested in automorphism groups of forms of even degree higher than two over ordered fields. In [A. Chlebowicz, A. Sładek, M. Wołowiec-Musiał, Automorphisms of certain forms of higher degree over ordered fields, Linear Algebra Appl. 331 (2001) 145–153] we proved that any group of order 2n containing a central involution is isomorphic with the orthogonal group of a certain form of degree 4n and we remarked that the degree 4n is grater than necessary. In this paper for any finite group G with a central involution we will construct a form of degree 8 with the orthogonal group isomorphic to G.