  We present a divisibility relation for the dimensions and Hilbert series of
certain classes of Nichols algebras of non-abelian group type, which
generalizes Nichols algebras over Coxeter groups with constant cocycle -1. For
this we introduce three groups of isomorphisms acting on Nichols algebras,
which generalize the exchange operator introduced by Milinski and Schneider for
Coxeter groups in "Pointed indecomposable Hopf algebras over Coxeter groups".
