Consider our axioms G₁, G₂, and G₃ for a group. We gave them in the order G₁, G₂, and G₃. Conceivable other orders to state the axioms are G₁G₃ G_2, G₂ G₁G_3, G₂ G₃ G_1. G₃ G₁ G₂, and G₃ G₂ G₁. Of these six possible orders, exactly three are acceptable for a definition. Which orders are not acceptable, and why?

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