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Answer :
Final answer:
The best possible value of |XY| is 84.
Explanation:
To find the best possible value of |XY|, we need to consider the orders of the subgroups X and Y. Given that XI=28 and [Y]=42, we can determine the possible values of |XY|.
Since the order of the intersection of two subgroups is the least common multiple (LCM) of the orders of the individual subgroups, we need to find the LCM of 28 and 42.
The prime factorization of 28 is 2^2 * 7, and the prime factorization of 42 is 2 * 3 * 7. To find the LCM, we take the highest power of each prime factor that appears in either factorization. Therefore, the LCM of 28 and 42 is 2^2 * 3 * 7 = 84.
Therefore, the best possible value of |XY| is 84.
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