Let p >= 5 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. In this paper we study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p, nu(1)) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over the polynomial algebra F-p[b], where b is a class of degree 2p + 2 defined as a "higher Bott element".
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