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(Dydak and Higes)\n  2) Suppose $G$ is a locally finite group with a proper left invariant metric $d_G$. If $\\dim_{AN}(G, d_G)>0$, is $\\dim_{AN} (G, d_G)$ infinite? (Brodskiy, Dydak and Lang)\n  The first question is answered positively not only for general metric spaces but also for discrete groups with proper left invariant metrics.\n  The second question has a negative solution. 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(Dydak and Higes)\n  2) Suppose $G$ is a locally finite group with a proper left invariant metric $d_G$. If $\\dim_{AN}(G, d_G)>0$, is $\\dim_{AN} (G, d_G)$ infinite? (Brodskiy, Dydak and Lang)\n  The first question is answered positively not only for general metric spaces but also for discrete groups with proper left invariant metrics.\n  The second question has a negative solution. 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