On the Same $n$-Types for the Wedges of the Eilenberg-Maclane Spaces

Given a connected CW-space $X, SNT(X)$ denotes the set of allhomotopy types $[X'']$ such that the Postnikov approximations$X^{(n)}$ and $X''^{(n)}$ are homotopy equivalent for all $n$. Themain purpose of this paper is to show that the set of all the samehomotopy $n$-types of the suspension of the wedges of theEilenberg-MacLane spaces is the one element set consisting of asingle homotopy type of itself, i.e., $SNT(Sigma (K(Bbb Z, 2a_1)vee K(Bbb Z, 2a_2) vee cdots vee K(Bbb Z, 2a_k))) = *$ for$a_1 < a_2 < cdots < a_k$, as a far more general conjecture thanthe original one of the same $n$-type posed by McGibbon andM{o}ller (in [McGibbon, C. A. and M{o}ller, J. M., On infinitedimensional spaces that are rationally equivalent to a bouquet ofspheres, Proceedings of the 1990 Barcelona Conference on AlgebraicTopology, Lecture Notes in Math., {bf 1509}, 1992, 285--293].)