  This article reviews and extends recent results concerning entanglement and
frustration in multipartite systems which have some symmetry with respect to
the ordering of the particles. Starting point of the discussion are Bell
inequalities: their relation to frustration in classical systems and their
satisfaction for quantum states which have a symmetric extension. It is then
discussed how more general global symmetries of multipartite systems constrain
the entanglement between two neighboring particles. We prove that maximal
entanglement (measured in terms of the entanglement of formation) is always
attained for the ground state of a certain nearest neighbor interaction
Hamiltonian having the considered symmetry with the achievable amount of
entanglement being a function of the ground state energy. Systems of Gaussian
states, i.e. quantum harmonic oscillators, are investigated in more detail and
the results are compared to what is known about ordered qubit systems.
