10Ma5aHw4 - topics are covered in class will some times...

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Ma 5 a HOMEWORK ASSIGNMENT 4 FALL 2010 INSTRUCTOR: D. RAMAKRISHNAN 278 SLOAN × 4348 It is advisable to do all the problems. But the only ones which need to be turned in are the five which are underlined and in bold, like 14 . Give details; part of what one must learn is the art of describing logical reasoning precisely and with no gaps. The exercises are taken from the text, Abstract Algebra (third edition) by Dummitt and Foote. This week, the problems taken from section 3.2 of the text (pages 95 , 96) concern themselves with Lagrange’s theorem, which will be discussed in class using the H -action on G for any subgroup H of a group G . (The order in which the
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Unformatted text preview: topics are covered in class will some times differ from that of the text, and the proofs will often be different.) The most important thing to become familiar with at this point in the course is to understand what constitutes an action of a group on a set and be able to deduce consequences. We will exploit G-sets as much as possible to prove results on groups. 1. Assignment 4 (due on Tuesday, October 26, by 4 PM) Page 65 , 66: 5, 8, 9, 10, 15, 16 , 18, 19 Pages 71 , 72: 2, 8, 11 , 14, 15, 17 Pages 85-89: 1, 4, 11, 12 , 16, 17, 18 , 25, 34, 36 Pages 95 , 96: 10, 19, 20, 21 Page 101: 3 , 8, 10 1...
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