problems-4-224-S08

# problems-4-224-S08 - MATH 224 PROBLEM SET 4 DUE 19 FEBRUARY...

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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. § 4.8–4.10. 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 FEBRUARY...

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