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N. Illinois | MATH 520
Algebra I

#### 13 sample documents related to MATH 520

• N. Illinois MATH 520
MATH 520 Prof. John Beachy Homework II 9/5/2007 Due 9/16/2007 1. (1.3, p 43, #4) Let p, q be distinct prime numbers, and let n = pq. In Z , let H = {[a]|a 1 (mod p)} and n K = {[b] | b 1 (mod q)}. Show that HK = Z . n 2. (1.3, p 44, #6) Let a, b

• N. Illinois MATH 520
Math 520 Review for the Final 12/10/07 Some general comments: we have covered a lot of material, and you have done a lot of homework problems. I think you are all pretty well prepared for the comprehensive exams over 520. The nal will have 50 poin

• N. Illinois MATH 520
MATH 520 Prof. John Beachy Homework IX Due 12/07/07 11/19/07 4.3 #1: In Example 4.3.3 use a direct calculation to verify that the subeld xed by 3 is Q( 4 2 i 4 2). 4.3 #2: In Example 4.3.3 determine which subelds are conjugate, and in each cas

• N. Illinois MATH 520
MATH 520 Prof. John Beachy Homework VI 10/15/2007 2.6 p102 #1: Let G be a group and let N be a normal subgroup of G. For a, b G, let [a, b] denote the commutator aba1 b1 . (a) Show that g[a, b]g 1 = [gag 1 , gbg 1 ]. (b) Show that N is a normal s

• N. Illinois MATH 520
MATH 520 Prof. John Beachy Homework III 9/12/2007 Due 9/21/2007 1. (2.1, p67 #8): Let X be an abelian group, and let G be any group. Find necessary and sucient conditions to | guarantee that the semidirect product X G is abelian. 2. (2.1, p67 #14

• N. Illinois MATH 520
MATH 520 Prof. John Beachy Midterm Exam 10/6/2004 The rst examination is scheduled for Friday, October 15. It will cover sections 1.11.4 and 2.12.7. Since sections 1.1 and 1.2 are really a review, you should read them, but dont expect specic quest

• N. Illinois MATH 520
MATH 520 Prof. John Beachy Homework I 8/29/2007 Due 9/05/2007 1. (1.1, p22, #7) Let G be a set with an associative binary operation . Prove that G is a group if (i) there exists a left identity e G such that e a = a for each a G, and (ii) for e

• N. Illinois MATH 520
MATH 520 EXAM I Professor J. Beachy, 9/25/98 1. (20 pts) Prove the Second Isomorphism Theorem. That is, let G be a group, let N be a normal subgroup of G, and let K be any subgroup of G. Prove that K N is a normal subgroup of K, and that KN/N is is

• N. Illinois MATH 520
MATH 520 MIDTERM EXAM J. Beachy, 10/22/2004 Choose 5 of the following 6 questions. Each one is worth 20 points. If you cannot complete a proof, you can get partial credit by stating the relevant denitions and results. In the computational examples

• N. Illinois MATH 520
ABSTRACT ALGEBRA: REVIEW PROBLEMS ON GROUPS AND GALOIS THEORY John A. Beachy Northern Illinois University 2006 ii This is a supplement to Abstract Algebra, Third Edition by John A. Beachy and William D. Blair ISBN 1577664434, Copyright 2006 Wavela

• N. Illinois MATH 520
MATH 520 Prof. John Beachy Homework VI Due 11/8/2004 10/29/2004 This set of problems is worth 50 points. You may use the library (or internet) but may not discuss the problems with anyone (in the class or not). 1. (10 pts; Section 3.3 #7) Let K be

• N. Illinois MATH 520
MATH 520 Prof. John Beachy Homework II 8/27/2004 Due 9/13/2004 1. (1.3, p 41, #5) Let p, q be distinct prime numbers, and let n = pq. In Zn , let H = {[a]|a 1 (mod p)} Show that HK = Zn . and K = {[b] | b 1 (mod q)}. 2. (1.3, p 41, #8) Thi

• N. Illinois MATH 520
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