  We consider a system of three particles in dimension 4 and higher interacting
via short-range potentials, where the two-body Hamiltonians have a virtual
level at the bottom of the essential spectrum. In dimensions 2 (in case of
fermions) and 3 the corresponding three-body Hamiltonian admits an infinite
number of bound states, which is known as the Efimov effect. In this work we
prove that this is not the case in higher dimensions. We investigate how the
dimension and symmetries of the system influence this effect and prove the
finiteness of the discrete spectrum of the corresponding three-body
Hamiltonian.
