13. Find groups that contain elements a and b such that Jal = \b| = 2 and a. Jab| = 3, b. Jab| = 4, c. \ab| = 5. Can you see any relationship among lal, [b|, and lab|? 14. Suppose that H is a proper...

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Extracted text: 13. Find groups that contain elements a and b such that Jal = \b| = 2 and a. Jab| = 3, b. Jab| = 4, c. \ab| = 5. Can you see any relationship among lal, [b|, and lab|? 14. Suppose that H is a proper subgroup of Z under addition and H contains 18, 30, and 40. Determine H.