  We study theoretically the transmission through a quantum dot molecule
embedded in the arms of an Aharonov-Bohm four quantum dot ring threaded by a
magnetic flux. The tunable molecular coupling provides a transmission pathway
between the interferometer arms in addition to those along the arms. From a
decomposition of the transmission in terms of contributions from paths, we show
that antiresonances in the transmission arise from the interference of the
self-energy along different paths and that application of a magnetic flux can
produce the suppression of such antiresonances. The occurrence of a period of
twice the quantum of flux arises to the opening of transmission pathway through
the dot molecule. Two different connections of the device to the leads are
considered and their spectra of conductance are compared as a function of the
tunable parameters of the model.
