MAT-3110 Midterm: MATH 3110 App State Fall2015 Test3 answer key
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Name: answer key: (15 points) getting things in order. Be sure to show your work! (a) let g = a4 d3 where a4 = {(1), (123), (132), (124), (142), (134), (143), (234), (243), (12)(34), (13)(24), (14)(23)} and. D3 = hx, y | x3 = 1, y2 = 1, xyxy = 1i = {1, x, x2, y, xy, x2y}. The order of g is |g| = |a4 d3| = |a4| |d3| = 12 6 = 72. Give an example of such an element and explain why it has the largest possible order. The orders of the elements in a4 are 1, 2 (eg. (12)(34)), and 3 (eg. The orders of the elements in a4 are 1, 2 (eg. (12)(34)), and 3 (eg. (123)). In d3 there are elements of orders 1, 2 (the re ections), and 3 (the non-trivial rotations) as well. Recall that in a direct product group we have:
