Published online by Cambridge University Press: 20 January 2009
Throughout this paper, we work in the category of (p-localized) spaces having the homotopy type of connected CW-complexes of finite type with base point. We consider a principal bundle
where Gn = SU(n), U(n) or Sp(n) and d = 1, 1 or 2 respectively. In this case, the bundle is obtained as an induced bundle by a mapping f of base space S2dn−1 from the classical group extension as follows: