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The electronic transport in a system of two quantum rings side-coupled to aquantum wire is studied via a single-band tunneling tight-binding Hamiltonian.We derived analytical expressions for the conductance and spin polarizationwhen the rings are threaded by magnetic fluxes with Rashba spin-orbitinteraction. We show that by using the Fano and Dicke effects this system canbe used as an efficient spin-filter even for small spin orbit interaction andsmall values of magnetic flux. We compare the spin-dependent polarization ofthis design and the polarization obtained with one ring side coupled to aquantum ring. As a main result, we find better spin polarization capabilitiesas compared to the one ring design

Fano and Dicke effects and spin polarization in a double Rashba-ring system side coupled to a quantum wire