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Let $[\rho_{i_k},[\rho_{i_{k-1}},...,[\rho_{i_{1}}, \rho_{i_2}] ...]]$ be aniterated 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 infinitequaternionic projective space. In this paper, it is shown that the image of thehomomorphism induced by the adjoint of this commutator is both primitive anddecomposable. The main result in this paper asserts that the set of allhomotopy types of spaces having the same $n$-type as the suspension of theinfinite quaternionic projective space is the one element set consisting of asingle homotopy type. Moreover, it is also shown that the group$\text{Aut}(\pi_{\leq n} (\Sigma {\Bbb H}P^\infty)/\text{torsion})$ ofautomorphisms is finite for $n \leq 9$, and infinite for $n \geq 13$, and that$\text{Aut}(\pi_{*} (\Sigma {\Bbb H}P^\infty)/\text{torsion})$ becomesnon-abelian.

On the same $N$-type of the suspension of the infinite quaternionic projective space