I am using the Borel transgression theorem as given in Mimura and Toda's "Topology of Lie groups I and II", page 378, Theorem 2.7. I know that it applies when the fiber has the homotopy type of a compact Lie group, but want to know if there are other classes of topological groups that satisfy the following condition:
There are transgressive homogeneous elements $x_i$ such that the natural map from the graded algebra over the $x_i$ to $H^{*}(G)$ is bijective up for degrees $\leq N$ and injective for higher degrees.
I would appreciate any references!
