problems-4-224-S08 - MATH 224 PROBLEM SET 4 DUE: 19...

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Unformatted text preview: MATH 224 PROBLEM SET 4 DUE: 19 FEBRUARY 2008 When you hand in this problem set, please indicate on the top of the front page how much time it took you to complete. Reading. 4.84.10. Problems from the book: 4.8.4, 4.8.8, 4.8.10, 4.8.16 1 4.9.1 Additional problems: 1. Let X = { 1,2,3,4 } . Write out all of the even permutations of X . Can you find a subset of four even permutations that is closed under composition? Is the composition of two even permutations even? Is the composition of two odd permutations odd? 2. A group is a non-empty set G together with a binary operation on G such that (Closure) For each g,h G , g h G ; (Associativity) For each g,h,k G , ( g h ) k = g ( h k ) ; (Identity) There exists an element e G such that e g = g e = g for every g G ; and (Inverses) For each g G there is a h G so that g h = h g = e . We write h = g- 1 ....
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problems-4-224-S08 - MATH 224 PROBLEM SET 4 DUE: 19...

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