hw11 - Exercise 7. For each of the following pairs , of...

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Modern Algebra 1 Homework 5.2 Spring 2010 Due February 17 Exercise 5. Let G be a group and for a,b G define a b if and only if there is an x G so that xax - 1 = b . Prove that is an equivalence relation on G . Exercise 6. Let n 2 and σ S n . Prove that σ ( a 1 a 2 ··· a k ) σ - 1 = ( σ ( a 1 ) σ ( a 2 ) ··· σ ( a k )). Use this to prove that two elements of S n are conjugate if and only if their cycle decompo- sitions have the same “cycle structure.”
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Unformatted text preview: Exercise 7. For each of the following pairs , of permutations, nd a permutation so that -1 = . a. = (15)(23), = (13)(45) b. = (123)(46)(78), = (135)(27)(48) c. = (123)(456), = (135)(246) Exercise 8. Compute Z ( Q ). [See homework 4.1 for the denition of Q .]...
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This note was uploaded on 02/29/2012 for the course MATH 3362 taught by Professor Ryandaileda during the Spring '10 term at Trinity University.

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