  The Cayley-Dickson loop Q_n 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, sedenions). We establish that the inner
mapping group Inn(Q_n) is an elementary abelian 2-group of order 2^(2^n-2) and
describe the multiplication group Mlt(Q_n) as a semidirect product of
Inn(Q_n)xZ_2 and an elementary abelian 2-group of order 2^n. We prove that
one-sided inner mapping groups Inn_l(Q_n) and Inn_r(Q_n) are equal, elementary
abelian 2-groups of order 2^(2^(n-1)-1). We establish that one-sided
multiplication groups Mlt_l(Q_n) and Mlt_r(Q_n) are isomorphic, and show that
Mlt_l(Q_n) is a semidirect product of Inn_l(Q_n)xZ_2 and an elementary abelian
2-group of order 2^n.
