MAT-3110 Final: MATH 3110 App State Spring2009 Final Exam
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Let r = {0, 3, 6, 9} z12. (a) finish lling out the following addition and multiplication tables for r: 0 (b) fill out the following table of information about r. R is a eld (c) fill out the following table concerning r. hint: these tables are longer than they need to be. /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). (b) find all of the left and right cosets of h in a4. Is h a normal subgroup of a4? (c) construct a cayley table for. /13 points) an ideal exam question. (a) find all of the principle ideals of z20. Hint: principle ideals of zn = cyclic subgroups of zn. (b) it turns out that z15 is a principle ideal of itself.
