MAT-3110 Midterm: MATH 3110 App State Fall2009 Test2
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/20 points) workin" mod 5. (a) fill out the following tables (don"t worry about brackets for equivalence classes. ) (z5, +) Z5 multiplication table (b) compute 2 1(4 + 3) 2 (mod 5). (c) find h3i (the subgroup generated by 3) in u (5) (not z5!!! (d) find the orders of elements of u (5). Why or why not? element = order = /16 points) quick proofs (a) let g be a group and suppose that x = x 1 for all x g. prove that g is abelian. Hint: xy = (xy) 1 = ? (b) let n be an integer such that n 3. /16 points) g = {1, a, a2, b, ab, a2b} is a group. Finish lling out g"s cayley table then answer some questions. 1 a a2 b ab a2b a2b a a. 1 a2b b ab a2 a2 ab a2b b b ab. 1 a2 ab ab a2b b a2 a2b a2b b ab.
