The Cayley-Dickson $Q_n$ loop is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley-Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, and sedenions).We discuss properties of the Cayley-Dickson loops, show that these loops are Hamiltonian, and describe the structure of their automorphism groups.
"Automorphism Groups of Cayley-Dickson Loops." J. Gen. Lie Theory Appl. 6 1 - 15, 2012.