To get the improper fraction of 10 5/12, multiply the denominator of the fraction and the number on the left which is 10x12=120. Then you want to add the numerator 5 to 120 to get 125. Using the denominator 12, and the numerator 125, there is your answer. 125/12.
Suppose first that is a normal subgroup. Then by definition we must have for all , for every . Let and choose (). By hypothesis we have , i.e. for some , thus . So we have . You can prove in the same way.
Suppose for all . Let , we have to prove for every . So, let . We have that for some (by the hypothesis). hence we have . Because was chosen arbitrarily we have the desired
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