A QUOTIENT OF THE SET [BG,BU(n)] FOR A FINITE GROUP G OF SMALL RANK

Let Gp be a Sylow p-subgroup of the finite groupG and let Char G n (Gp) represent the set of degree n complex characters of Gp that are the restrictions of class functions on G. We construct a natural map ψG : [BG,BU(n)] → ∏ p||G| Char G n (Gp) and prove that ψG is a surjection for all finite groups G that do not contain a subgroup isomorphic to (Z/p) for any prime p. We show, furthermore, that ψG is in fact a bijection for two types of finite groups G: those with periodic cohomology and those of odd order that do not contain a subgroup isomorphic to (Z/p) for any prime p. 2000 MSC: 55R37, 55S35, 20J06, 20D15