  Metric components of potentials of admissible electromagnetic fields in
spaces with simply transitive four-parameter motion group are found. The
components of frame vectors corresponding to the components of the metric
tensors found by Petrov are given. The results obtained complement the
coordinate-free classification given by Magazev et al. Previously, admissible
electromagnetic fields were found for the case when three- and four-parameter
groups of motions act on hypersurfaces of spacetime. Thus, non-equivalent sets
of potentials for all electromagnetic fields that admit three- and
four-parameter groups of motions are known now.
