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Let Qn be the quaternionic quasi-projective space (cf. [11]). Then it is a 2-connected CW-complex having one 4f— 1 dim cell for each i with l<Li<n. It is known that the order of the cokernel of the stable Hurewicz homomorphism h: ^In-i(On)->//in-i(On ; Z) is equal to a(n-l)-(2n-l}\ (see Theorem 3.10), where and throughout the paper a(i) denotes 1 if i is an even integer and 2 if i is an odd integer. Then, for any generator x of the free part of nln-i(Qn\ the modp Adams filtration Fp(x) is less than or equal to up(a(n— l)-(2n— 1)!), where vp(j) denotes the exponent of a prime p in the prime power decomposition of an integer /. Let GCp) denote the tensor product G®Z(P) for an abelian group G, where ZCp) is the ring of integers localized at p. Then, one of the results in this note is the following.

On the Adams filtration of a generator of the free part of {$\pi\sp s\sb *(Q\sb n)$}