  In generic dynamical systems heteroclinic cycles are invariant sets of
codimension at least one, but they can be structurally stable in systems which
are equivariant under the action of a symmetry group, due to the existence of
flow-invariant subspaces. For dynamical systems in R^n the minimal dimension
for which such robust heteroclinic cycles can exist is n=3. In this case the
list of admissible symmetry groups is short and well-known. The situation is
different and more interesting when n=4. In this paper we list all finite
groups Gamma such that an open set of smooth Gamma-equivariant dynamical
systems in R^4 possess a very simple heteroclinic cycle (a structurally stable
heteroclinic cycle satisfying certain additional constraints). This work
extends the results which were obtained by Sottocornola in the case when all
equilibria in the heteroclinic cycle belong to the same Gamma-orbit (in this
case one speaks of homoclinic cycles).
