  In the reactions $p\bar p\to\pi^0\pi^0,\eta\eta,\eta\eta'$ there are four
relatively narrow resonances $f_2(1920)$, $f_2(2020)$, $f_2(2240)$,
$f_2(2300)$, and a broad one $f_2(2000)$ in the mass region 1990--2400 MeV. In
the framework of quark combinatorics we carry out an analysis of the decay
constants for all five resonances. It is shown that the relations for the decay
constants corresponding to the broad resonance
$f_2(2000)\to\pi^0\pi^0,\eta\eta, \eta\eta'$ are the same as those
corresponding to a glueball. An additional argument in favour of the
glueball--nature of $f_2(2000)$ is the fact that $f_2(1920)$, $f_2(2020)$,
$f_2(2240)$, $f_2(2300)$ fit well the $q\bar q$ trajectories in the
$(n,M^2)$-plane (where $n$ is the radial quantum number), while the broad
$f_2(2000)$ resonance turns out to be an unnecessary extra state for these
trajectories.
