On pointed Hopf algebras associated with alternating and dihedral groups

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We classify finite-dimensional complex pointed Hopf algebra with group of group-like elements isomorphic to A₅. We show that any pointed Hopf algebra with infinitesimal braiding associated with the conjugacy class of π ∈ Aₙ is infinite-dimensional if the order of π is odd except for π=(1 2 3) in A₄. We also study pointed Hopf algebras over the dihedral groups.