MAT-3110 Midterm: MATH 3110 App State Spring2010 Test2
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/20 points) random group stu fill out the following table: , x6y} where x7 = 1, y2 = 1, and xyxy = 1. If g is a group, prove it you may use a subgroup test if it applies. If g fails to be a group, explain what property fails. (a) let g = [ 1, 1] = {r r | 1 r 1} with the operation + (addition). 1(cid:21) (cid:12)(cid:12)(cid:12) (b) let g = (cid:26)(cid:20)1 0 r r r(cid:27) with the operation of matrix multiplication. Recall that dn = {1, x, x2, . , xn 1y} where xn = 1, y2 = 1, and xyxy = 1. (a) write down what the left multiplication operator of y does in d3. Then write down the corre- sponding permutation if we label 1 as 1, x as 2, x2 as 3, y as 4, xy as 5, x2y as 6.
