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Low lying states of a vertically coupled three-layer quantum-dot system are studied. Each layer contains oneelectron, and the tunnelling of electrons between layers is neglected. Effects of the interlayer separation d and theexteal magnetic field B are evaluated by numerical calculations. In the strong coupling case (i.e. d is small),as in a single dot, transitions of the angular momentum L of the true ground states occur when B increases,whereas in the weak coupling case the transition does not occur and L remains zero. Furthermore, it is foundthat the variation of d may also induce the L transition. As a result, a phase diagram of L of the true groundstate is given in the d - B plane.