This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 nonempty 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 ....
View
Full
Document
 Spring '08
 TARAHOLM

Click to edit the document details