On the radical of cluster tilted algebras

We determine the minimal lower bound n, with $$n \geqslant 1$$ , where n-th power of radical module category a representation-finite cluster tilted algebra vanishes. give such in terms number vertices underline quiver. Consequently, we get nilpotency index for self-injective algebras. also study non-zero composition m, $$m 2$$ irreducible morphisms between indecomposable modules algebras lying $$(m\,{+}\,1)$$ -th their category.