  We present a theoretical study of the spectrum of electrons confined in
triple concentric rings. An unusual ordering and rich variety of angular
momentum transitions are found that depend on the coupling between the rings
and the confinement potential of the rings. Using the Configuration Interaction
(CI) method, we calculated the two electron energy spectrum. Spin singlet to
spin triplet transitions of the electron ground state are predicted and a
fractional Aharonov-Bohm effect is found. We show that both the period and
amplitude of the spin singlet - triplet energy gap depend strongly on the
confinement potential and the external magnetic field. The spin singlet -
triplet transition is found to depend on the spin Zeeman energy, especially for
rings with weak confinement and in the presence of large magnetic field. The
amplitude of the spin singlet - triplet energy gap depends on the Land\'{e}
$g$-factor but the period of the transitions is independent of $g$.
