  Starting from some ideas given by Bales in [Ba; 09], in this paper we present
an algorithm for computing the elements of the basis in an algebra obtained by
the Cayley-Dickson process. As a consequence of this result, we prove that an
algebra obtained by the Cayley-Dickson process is a twisted group algebra for
the group G = Zn2 ; n = 2t, t 2 N, over a field K, with charK = 0. In the last
section, we give some properties and applications of the quaternion
nonassociative algebras.
