Divisible groups in the K-theory completion of SU(n)

Results of Bendersky and Thompson for the E(1)-based E2 -term of S2n+1, and the results of Bendersky and Davis concerning the v1-periodic groups of SU(n) are used to compute the E(1)-based E2-term for SU(n) at odd primes. This computation is performed using the Bendersky Thompson spectral sequence for SU(n). For spaces like SU(n) this spectral sequence converges to homotopy groups of the K-theory completion of SU(n). Of particular interest, is the existence of infinitely many divisible groups in the homotopy groups of the K-theory completion of SU which offers an example of how E-completion does not commute with direct limits.