  We compute the 3-primary v1-periodic homotopy groups of the exceptional Lie
group E7. Now E8 at the primes 3 and 5 is the only compact simple Lie group
whose odd-primary v1-periodic homotopy groups remian to be computed. The main
work is computing the unstable Novikov spectral sequence of \Omega E7/Sp(2).
Showing that this converges to v1-periodic homotopy groups requires recent work
of Bousfield and Bendersky-Thompson.
