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Lepton number violation decay omega -> pi(+) pi(+)e(-) e(-)+c. c.* is searched for via J/psi -> omega eta using a data sample of (1. 0087 +/- 0.0044) x 10(10) J/psi events collected via the BESIII detector at the BEPCII collider. No significant signal is observed, and the upper limit on the branching fraction of omega -> pi(+) pi(+)e(-) e(-)+c. c. at the 90% confidence level is determined for the first time to be 2.8 x 10(-6). .