We compute necessary conditions on Yetter-Drinfeld modules over the groups
\mathbf{PGL}(2,q)=\mathbf{PGL}(2,\FF_q) and
\mathbf{PSL}(2,q)=\mathbf{PSL}(2,\FF_q) to generate finite dimensional
Nichols algebras. This is a first step towards a classification of pointed Hopf
algebras with group of group-likes isomorphic to one of these groups.
As a by-product of the techniques developed in this work, we prove that there
is no non-trivial finite-dimensional pointed Hopf algebra over the Mathieu
groups M20 and M21=PSL(3,4).Comment: Minor change