  We show that the existence of a dense set of periodic points for a
topologically transitive non-minimal continuous group action on a Hausdorff
uniform space with an infinite acting group does not necessarily imply a
sensitive dependence to the initial conditions in such a system. This leads to
define the chaos in the sense of Devaney for a continuous group action on a
Hausdorff uniform spaces with an infinite acting group in the original way,
i.e. a non-minimal topologically transitive and sensitive system with a dense
set of periodic points is a chaotic system in the sense of Devaney.
