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In this work, we study the charged lepton flavor violating (cLFV) decays$\tau-> \mu\gamma$, $\tau-> 3\mu$ and $Z->\mu\tau$ in the framework of theSupersymmetric economical 3-3-1 model. Analytic formulas for branching ratios(BR) of these decays are presented. We assume that there exist lepton flavorviolation (LFV) sources in both right- and left-handed slepton sectors. Thisleads to the strong enhancement of cLFV decay rates. We also show that theeffects of the LFV source to the cLFV decay rates in the left-handed sleptonsector are greater than those in the right- handed slepton sector. By numericalinvestigation, we show that the model under consideration contains the relativelight mass spectrum of sleptons which satisfies the current experimental boundson LFV processes in the limit of small $\tan \gamma$. The interplay betweenmonopole and dipole operators also was studied.

Lepton flavor violating processes \tau ->\mu\gamma$, $\tau-> 3\mu$ and $Z-> \mu\tau$ in the Supersymmetric economical 3-3-1 model