MAT-3110 Midterm: MATH 3110 App State Fall2011 Test3

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15 Feb 2019
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/25 points) 3-2-1go! (a) how many elements of order 3 are in z9000 z3333333? (b) let h be a subgroup of g where g is abelian. Quickly explain why h is a normal subgroup of g. (c) consider for example: Now let k = n (where k, , n are positive integers) and let. Brie y, explain why the g has order k, why g is cyclic, and why g = zk. (d) let g and h be group. Prove that : g h g de ned by ((g, h)) = g is a homomorphism which is onto. /25 points) quotients (a) given: k = {r0, r180} is a normal subgroup of d6. The size of the set r60k is (b) let h be a (normal) subgroup of g where g is abelian. H is abelian. (c) consider where h = h4i = {0, 4, 8}. List all of the cosets (and their contents).

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