MAT-3110 Final: MATH 3110 App State Spring2009 Final Exam answer key
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May 4th, 2009: (12 points) tables for sarah. Let r = {0, 3, 6, 9} z12. (a) finish lling out the following addition and multiplication tables for r: 9 (b) fill out the following table of information about r. Notice that 9x = x = x9 for all x. 6 is not a unit. (c) fill out the following table concerning r. hint: these tables are longer than they need to be. 3 1 = 3 since 3 3 = 9 (the identity). 9 1 = 9 since 9 9 = 9 (the identity): (13 points) recall a4 = {(1), (123), (132), (124), (142), (134), (143), (234), (243), (12)(34), (13)(24), (14)(23)}. Let h = {(1), (12)(34), (13)(24), (14)(23)}. (a) quickly explain why h is a subgroup of a4 (i am thinking of a certain one word answer). If you think about this for a moment, you should realize that you only need to perform a few permutation compositions.
