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We study the decays $\Lambda_{c}^{+}\to\Lambda\eta\pi^{+}$ and$\Sigma(1385)^{+}\eta$ based on $\Lambda_{c}^{+}\bar{\Lambda}_{c}^{-}$ pairsproduced in $e^+e^-$ collisions at a center-of-mass energy of$\sqrt{s}=4.6~\mbox{GeV}$, corresponding to an integrated luminosity of$567\;\mbox{pb$^{-1}$}$. The data sample was accumulated with the BESIIIdetector at the BEPCII collider. The branching fractions are measured to be$\mathcal{B}(\Lambda_{c}^{+} \to\Lambda\eta\pi^{+})=(1.84\pm0.21({\rm{stat.}})\pm0.15({\rm{syst.}}))\%$ and$\mathcal{B}(\Lambda_{c}^{+} \to\Sigma(1385)^{+}\eta)=(0.91\pm0.18({\rm{stat.}})\pm0.09({\rm{syst.}}))\%$,constituting the most precise measurements to date.

Measurement of the absolute branching fractions of $\Lambda_{c}^{+}\to\Lambda\eta\pi^{+}$ and $\Sigma(1385)^{+}\eta$