MATH 4023 Midterm: MATH 4023 LSU 04Exam 3a
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Answer each of the questions on your own paper, and be sure to show your work so that partial credit can be adequately assessed. Put your name on each page of your paper: [16 points] find the order of each of the following group elements. Justify your answer either by a calculation or by reference to an appropriate theorem. (a) the element 2 in the group z . 22 = 4, 23 = 8, 24 = 5, 25 = 10 = 1, 26 = 2 = 9, 27 = 4 = 7, 11| = 10, lagrange"s theorem shows that the order of each element divides 10. Hence o(2) is 1, 2, 5, or 10. From the calculations above, 22 = 4 6= 1, and 25 = 10 6= 1. Hence the order of 2 is not 1, 2 or 5, so it must be 10.
