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Abstract. Let X be a space of finite type. Set q = 2(p−1) as usual, and define the mod q support of K(n) ∗ ⊕ (X) byS(X, K(n)) = {m ∈ Z/qZ | d≡m mod q K(n)d = 0} for n> 0. Call K(n) ∗ (X) sparse if there is no m ∈ Z/qZ with m, m +1 ∈ S(X, K(n)). Then we show the relation S(X, K(n)) � S(X, K(n+1)) for any finite type space X with K(n +1) ∗ (X) being sparse. As a special case, we have K(n +1) odd (X) =0= ⇒ K(n) odd (X) =0, and the main theorem of Ravenel, Wilson and Yagita is also generalized in terms of the mod q support

Year: 2013

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