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We consider SPT-phases with on-site finite group $G$ symmetry $\beta$ fortwo-dimensional quantum spin systems. We show that they have $H^{3}(G,{\mathbbT})$-valued invariant.

A $H^{3}(G,{\mathbb T})$-valued index of symmetry protected topological  phases with on-site finite group symmetry for two-dimensional quantum spin  systems