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Entanglement between n particles is a generalization of the entanglement between two particles, and a state is considered entangled if it cannot be written as a mixture of tensor products of the n particles' states. We present the key notion of semi-separability, used to investigate n-particle entanglement by looking at two-subsystem entanglement between its various subsystems. We provide necessary conditions for n-particle separability (that is, sufficient conditions for n-particle entanglement). We also provide necessary and sufficient conditions in the case of pure states. By a surprising example, we show that such conditions are not sufficient for separability in the case of mixed states, suggesting entanglement of a strange type.