LAUSR

Let G be a group which admits a generating set consisting of finite order elements. We prove that any Hopf algebra which factorizes through the Taft algebra and the group Hopf algebra K[G] (equivalently, any bicrossed product between the aforementioned Hopf algebras) is isomorphic to a smash product between the same two Hopf algebras. The classification of these smash products is shown to be strongly linked to the problem of describing the group automorphisms of G. As an application, we completely describe by generators and relations and classify all bicrossed products between the Taft algebra and the group Hopf algebra $$K[D_{2n}]$$K[D2n], where $$D_{2n}$$D2n denotes the dihedral groups.