Based on a sample of $2.25times 10^{8} J/psi$ events taken with the BESIII detector at the BEPCII collider, we present the results of a study of the decay $J/psito eta phipi^{+}pi^{-}$. The $Y(2175)$ resonance is observed in the invariant mass spectrum of $phi f_{0}(980)$ with a statistical significance of greater than $10sigma$. The corresponding mass and width are determined to be $M=2200pm 6 mathrm{(stat.)} pm 5mathrm{(syst.)} mathrm{MeV}/c^{2}$ and $Gamma=104pm 15mathrm{(stat.)}pm 15mathrm{(syst.)}$ MeV, respectively, and the product branching fraction is measured to be $mathcal{B}(J/psitoeta Y(2175)$, $Y(2175)to phi f_{0}(980)$, $f_{0}(980)to pi^{+}pi^{-})= (1.20pm 0.14mathrm{(stat.)}pm 0.37 mathrm{(syst.)})times 10^{-4}$. The results are consistent within errors with those of previous experiments. We also measure the branching fraction of $J/psito phi f_1(1285)$ with $f_1(1285)to etapi^{+}pi^{-}$ and set upper limits on the branching fractions for $J/psito phieta(1405)$/$phi X(1835)$/$phi X(1870)$ with $eta(1405)$/$X(1835)$/$X(1870)to etapi^{+}pi^{-}$ at the 90% confidence level.
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