  Let $[\rho_{i_k},[\rho_{i_{k-1}},...,[\rho_{i_{1}}, \rho_{i_2}] ...]]$ be an
iterated commutator of self-maps $\rho_{i_j} : \Sigma {\Bbb H}P^\infty \to
\Sigma {\Bbb H}P^\infty, j = 1,2, ..., k$ on the suspension of the infinite
quaternionic projective space. In this paper, it is shown that the image of the
homomorphism induced by the adjoint of this commutator is both primitive and
decomposable. The main result in this paper asserts that the set of all
homotopy types of spaces having the same $n$-type as the suspension of the
infinite quaternionic projective space is the one element set consisting of a
single homotopy type. Moreover, it is also shown that the group
$\text{Aut}(\pi_{\leq n} (\Sigma {\Bbb H}P^\infty)/\text{torsion})$ of
automorphisms is finite for $n \leq 9$, and infinite for $n \geq 13$, and that
$\text{Aut}(\pi_{*} (\Sigma {\Bbb H}P^\infty)/\text{torsion})$ becomes
non-abelian.
