  We find all the perfect fluid G2 diagonal cosmologies with the property that
the quotient of the norms of the two orthogonal Killing vectors is constant
along each fluid world-line. We find four different families depending each one
on two or three arbitrary parameters which satisfy that the metric coefficients
are not separable functions. Some physical properties of these solutions
including energy conditions, kinematical quantities, Petrov type, the existence
and nature of the singularities and whether they contain
Friedman-Robertson-Walker cosmologies as particular cases are also included.
