  We study the parameterized complexity of a robust generalization of the
classical Feedback Vertex Set problem, namely the Group Feedback Vertex Set
problem; we are given a graph G with edges labeled with group elements, and the
goal is to compute the smallest set of vertices that hits all cycles of G that
evaluate to a non-null element of the group. This problem generalizes not only
Feedback Vertex Set, but also Subset Feedback Vertex Set, Multiway Cut and Odd
Cycle Transversal. Completing the results of Guillemot [Discr. Opt. 2011], we
provide a fixed-parameter algorithm for the parameterization by the size of the
cutset only. Our algorithm works even if the group is given as a
polynomial-time oracle.
