  We verify that universal classes in the cohomology of $GL_N$ determine
explicit cohomology classes of Frobenius kernels $G_{(r)}$ of various linear
algebraic groups $G$ . We consider the relationship of $\varprojlim_r
H^*(U_{(r)},k)$ to the rational cohomology $H^*(U,k)$ of many unipotent
algebraic groups $U$. The second half of this paper investigates in detail the
cohomology of Frobenius kernels $(U_3)_{(r)}$ of the Heisenberg group $U_3
\subset GL_3$.
