The group inverse of a companion matrix

@inproceedings{Puystjens1997TheGI,
  title={The group inverse of a companion matrix},
  author={Roland Puystjens and R. E. Hartwig},
  year={1997}
}
A complete characterization is given for the group inverse of a companion matrix over an arbitrary ring to exist. Formulae are given for the actual group inverse and some consequences are drawn.