  We construct nonlinear multiparty entanglement measures for distinguishable
particles, bosons and fermions. In each case properties of an entanglement
measures are related to the decomposition of the suitably chosen representation
of the relevant symmetry group onto irreducible components. In the case of
distinguishable particles considered entanglement measure reduces to the
well-known many particle concurrence. We prove that our entanglement criterion
is sufficient and necessary for pure states living in both finite and infinite
dimensional spaces. We generalize our entanglement measures to mixed states by
the convex roof extension and give a non trivial lower bound of thus obtained
generalized concurrence.
