# Elements of large order in pi_*(SU(n))

## Donald M. Davis

To appear in Topology. Last updated July 5, 1996. 50 pages long.
### Abstract

It is proved that if p is an odd prime, then some homotopy group of SU(n)
contains an element of order p^e, where e = n-1+[(n+2p-3)/p^2]+[(n+p^2-p-1)/p^3]
. The method is to compute v1-periodic homotopy groups, using the unstable
Novikov spectral sequence. This should be very close to the largest orders
of v1-periodic elements, and we conjecture that the elements of largest
order are v1-periodic.
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