Without using the Feit-Thompson theorem, show that the following statements are equivalent. (i) Every group of...

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Without using the Feit-Thompson theorem, show that the following statements are equivalent. (i) Every group of odd-order is solvable. (ii) The only simple groups of odd order are of prime order. Without using the Feit-Thompson theorem, show that the following statements are equivalent. (i) Every group of odd-order is solvable. (ii) The only simple groups of odd order are of prime order.

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