Corollary 7.3.11. Let \(X\) be a spectrum and let \(n \in \Z \) be such that \(\pi _n(X)\) and \(\pi _{n-1}(X)\) are finitely generated. Then there is an isomorphism \[ \pi _n(X^{\wedge }_p) \; \cong \; \pi _n(X) \otimes _{\Z } \Z _p. \]
Proof. By Lemma 7.3.9, the right-hand term of the short exact sequence of Theorem 7.3.10 vanishes, while its left-hand term is \(\pi _n(X) \otimes _{\Z } \Z _p\). □
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