Consider our axioms G 1 , G 2 , and G 3 for a group. We gave
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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 G2, G2 G1G3, G2 G3 G1. 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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