  In this article, we explicitly construct new finite-dimensional,
link-indecomposable Nichols algebras with Dynkin diagrams of type
An,Cn,Dn,E6,E7,E8,F4 over any group G with commutator subgroup isomorphic to
Z_2.The construction is generic in the sense that the type just depends on the
rank and center of G, and thus positively answers for all groups of this class
a question raised by Susan Montgomory in 1995 [Mont95][AS02].
  Our construction uses the new notion of a covering Nichols algebra as a
special case of a covering Hopf algebra [Len12] and produces non-faithful
Nichols algebras. However, we give faithful examples of Doi twists for type
A3,C3,D4,F4 over several nonabelian groups of order 16 and 32. These are hence
the first known examples of faithful, finite-dimensional, link-indecomposable
Nichols algebras of rank >2 over nonabelian groups.
