4200t2 - ). (2 pts) (vi) Write down a transposition that...

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Math 4200 Section 2/ Fall 2002 Test 2 Name: Please provide full explanations with your answers wherever necessary. In order to receive full credit, your work must be presented in a clean and formal way. 1. Let σ S 5 be the permutation given by σ = ± 1 2 3 4 5 4 5 1 3 2 (i) Write down the value of σ (2) (2pts) (ii) Write down the permutation σ - 1 . (3pts) (iii) Work out the permutation σ 2 . (5 pts)
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(iv) Write down the cycle decomposition of σ . (4 pts) (v) Work out, with explanation, sgn(
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Unformatted text preview: ). (2 pts) (vi) Write down a transposition that does not commute with . (2 pts) (vii) Express the cycle (135) as a product of transpositions. (2 pts) 2. Suppose G is a group in which the square of every element is the identity. Prove that G is commutative. (5pts) 3. Let G be a group of prime order (i.e. the number of elements in G is a prime number). Prove that G is cyclic. (5pts)...
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4200t2 - ). (2 pts) (vi) Write down a transposition that...

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