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Unformatted text preview: G denote a group having the just the 4 elements G = { a, b, c, d } . Suppose that ab = a and a 3 = c . (a) Which element of G is the identity. (b) ±ill in the multiplication table for G . (c) Is G isomorphic to Z 4 ? Is G isomorphic to Z 2 × Z 2 ? (4) Explain why each of the following pairs of groups are (or are not) isomorphic. (a) Z 6 and Z 2 × Z 3 . (b) S 3 and Z 6 . (c) S 4 and S 3 . (d) S 2 and Z 2 . 1 2 PRACTICE MIDTERM FOR MAT 312 (5) Consider the permutation σ ∈ S 8 defned by σ = (126)(8241)(5368). (a) Write σ as a 2 × 8 matix having 1 2 3 4 5 6 7 8 For frst row. (b) Write σ1 as a 2 × 8 matrix (as in part (a)). (c) Compute order ( σ ). (d) Write σ as a product oF disjoint cycles....
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 Fall '08
 BESCHER
 Algebra, Cryptography, Code word, Konrad Zuse

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