  Using Perron-Frobenius theorem, we prove that the results by Wilkin, Gunn and
Smith [1] for the ground states of N Bose atoms rotating at the angular
momentum L in a harmonic atomic trap with frequency omega interacting via
attractive delta^2(r) forces, are valid for a broad class of predominantly
attractive interactions V(r), not necessarily attractive for any r. The
sufficient condition for the interaction is that all the two-body matrix
elements <z_1^k z_2^l |V| z_2^m z_1^n> allowed by the conservation of angular
momentum k+l = m+n, are negative. This class includes, in particular, the
Gaussian attraction of arbitrary radius, -1/r - Coulomb and log(r)-Coulomb
forces, as well as all the short-range R << omega^{-1/2} interactions
satisfying inequality int d^2r V(r) < 0. There is no condensation at L>> 1, and
the angular momentum is concentrated in the collective ``center-of-mass'' mode.
