The number of summands in v1-periodic homotopy groups of SU(n)

In this work we determine the number of summands of v1−1π2k−1(SU(n);p) for all values of p, k, and n, where p is an odd prime. The method being used involves finding the rank of a family of matrices generated by the Adams operations. Determining the group structure of v1−1π2k−1(SU(n);p) groups still remains an open question.