  We show that a wide class of spin chains with topological frustration cannot
develop any local order. In particular, we consider translational-invariant
one-dimensional chains with frustrated boundary conditions, i.e. periodic
boundary conditions and an odd number of sites, which possess a global SU(2)
symmetry. This condition implies, even at a finite sizes, an exact degeneracy
of the ground state and is quite general in absence of external fields. We
directly evaluate the expectation value of operators with support over a finite
range of lattice sites and show that, except for some precise conditions, they
all decay algebraically, or faster, with the chain length and vanish in the
thermodynamic limit. The exceptions that admit a finite order are cases with a
higher ground state degeneracy in which the translational symmetry is broken by
the ground state choice.
