CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

Abstract

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).