  Scalar glueball is implemented in single nonet linear sigma model (SNLSM)
which basically includes lowest lying scalar and pseudoscalar mesons. Our new
version of SNLSM involves mixing among scalar matter fields and glueball field
which is enforced by scale symmetry considerations and the associated anomaly.
Performing iterative Monte Carlo simulations, it is found that among the three
candidates of scalar glueball, i.e., $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$,
only $f_0(1500)$ is predominately a glueball state with the mass prediction of
$1.566 \pm 0.046$ GeV and the other two are predominately quarkonium. The
$\pi\pi$, $\pi K$ and $\pi \eta$ scatterings are reinvestigated in the presence
of scalar glueball and it is found that the overall behavior of the real part
of the K-matrix unitarized $\pi \pi$ scattering amplitude is more compatible
with observed data compared with the case of SNLSM without glueball. We have
also presented the predictions of the model for the masses and decay widths of
the scalars obtained from the poles of the K-matrix unitarized $\pi\pi$, $\pi
K$ and $\pi \eta$ scattering amplitudes. Moreover the $\pi\pi$ scattering phase
shift predicted by our model is compared with the prediction of generalized
linear sigma model (GLSM) which contains two nonets of scalar mesons and two
nonets of pseudoscalar mesons (a quark-antiquark nonet and a four-quark nonet).
Despite the fact that at this stage our model lacks the second meson nonet
above $1$ GeV, its prediction for the $\pi\pi$ scattering phase shift is close
to the prediction of GLSM for $\sqrt{s}<1.1$ GeV and in better agreement with
experimental data for $\sqrt{s}>1.1$ GeV in comparison with GLSM.
