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

Divisibility Relations for the Dimensions and Hilbert series of Nichols Algebras of Non-Abelian Group Type