ELEMENTS OF LARGE ORDER IN π∗(SU(n))

with e ≥ n− 1− [n+2p−3 p2 ] + [ 2−p−1 p3 ]. Computing homotopy groups is a notoriously difficult problem. The groups πi(S ) are known only for relatively small values of i− n, and quickly become quite complicated, but the celebrated exponent theorem of [7] showed expp(S ) = n for all odd primes p. Groups πi(SU(n)) have been computed for small values of i − n by many topologists, with all known results compiled in [12]. It was not until the work of the author in [9] that information about all homotopy groups of all SU(n) was obtained. There it was shown that