A note on the cohomology of finite dimensional cocommutative Hopf algebras
John H. Palmieri
In the context of finite dimensional cocommutative Hopf algebras, we
prove versions of various group cohomology results: the Quillen-Venkov
theorem on detecting nilpotence in group cohomology, Chouinard's
theorem on determining whether a $kG$-module is projective by
restricting to elementary abelian $p$-subgroups of $G$, and Quillen's
theorem which identifies the cohomology of $G$, ``modulo nilpotent
elements.'' This last result is only proved for graded connected Hopf
algebras.