# Tractable formulas for v_1-periodic homotopy groups of SU(n) if n < p^2-p+2

## Donald M. Davis and Huajian Yang

Last updated Feb. 1995.

### Abstract

Let p be a fixed odd prime. In [Davis, Proc LMS 1991], it was proved that for d=0 and 1, v_1^{-1}\pi_{2k-d}(SU(n)) has order p^{e(k,n)}, where e(k,n)=\min\{\nu_p(j!S(k,j)):n\le j\le k\}, with S(k,j) the Stirling number of the second kind. In this paper, we give a more tractable formula for e(k,n) when n < p^2-p+2 by calculating the unstable Novikov spectral sequence. We also determine the abelian group structure when d=1; it was known to be cyclic when d=0.