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MATH 731 Abstract Algebra II(Spring 2007) ()
Zongzhu Lin
MWF, 3:30pm-4:20pm, CW 130
 
ATTENDING CLASSES:  It should be clear that it is the students' responsibility to attend the classes at the scheduled time and place to get all announcements and handouts (including homework assignments with due dates), to take the exams, to hand in or take back your homework, and, of course, to listen to the lecture. The returning homework will be brought to class at most three consecutive class meetings and then will be sent to recycling services unless you have made prior arrangements with the instructor. If you have any concerns or special needs, please let me know as early as possible. Let me remind you that it is your responsibility to observe all deadlines for adding to or dropping from classes and to know the final exam time and room scheduled by the university.
EXAMS:   There will be one 50-minute midterm in-class exams in addition to a comprehensive 110-minute final exam and their schedules are listed below. The exam scores will be given on a percentage basis.
Mideterm Exam : TBA, TBA, 2006, in class.
Final Exam: Monday,  May 7, 4:10pm-6:00pm(Check the university final Exam schedule)
HOMEWORK: There will be two sets of problems (called HW and PRAC) assigned about every three lectures (about twelve in total). HW are homework problems, which students are required to do carefully and will be graded. PRAC are practice problems and many exam problems will be based on them. The homework grades will be taken into your final course grade. Warning: No joint homework or project will be accepted unless you are told to do so. Although you are strongly encouraged to form study groups and to discuss anything you want, but make sure that no one copies anything from others.
"CHEAT SHEET" About two week priior to the final exam, a special piece of paper will be distributed to every students in class. Students can write any useful information and bring it to the final exam to help them. The size is not large enough and special organization of the materials will be necessary. Students who missed or misused this piece of paper will have to take the final exam without a cheating sheet. No substitute will be allowed.
COURSE GRADE: Your course grade is calculated from the overall course score (%) by the following rules:A: 89-100, B: 77-88, C: 63-76, D: 50-62 and F: below 50. In principle, grades of any exams o homework will not be curved or converted to letter grades. The overall score is calculated by
Overall(%)=HWx25% + Midterm x 25% +FEx50%
REMARKS:  (1)  There will be no makeup exams to be given or late homework to be accepted unless you have the permission from the instructor before the due time or you have an emergency, such as illness, in such a case, doctor's proof (clearly indicating that it is an emergency) is necessary. However, the HW will be the average after dropping two of the lowest (%) grades (missing homework will be treated as 0).
(2) In your solutions to problems of exams or homework, you have to show your work and write them clearly (literally) for the grader to understand. The grader will not guess unless you write clearly. All grades will be given based on your presentation on the paper (no oral explanation afterwards will be counted).

Office Hours:  MWF 1:30pm--2:20pm or by appointment.
Office Location:    Cardwell Hall 210.  Tel.: 532-0573
Course Webpage:  http://www.math.ksu.edu/~zlin/m730
 
Text Book:  Algebra 1991 edition, by Michael Artin Published by Prentice Hall.  The book should be available in K-State Union Book Store.
 



Homework Assignments
Homework is due at the beginning of class of the due day.
HW No. Sections  Homework Problems  Practice Problems
Due Day
#1 1.1
1.2
 2(a), 7, 8, 10, 16
8, 13, 15, 17
 5,6,11,15,
10, 12,14,18
 F. 9/1
#2 1.3
1.4
1.5
misc
 4, 5, 10, 12
2, 5, 8
2,3
1, 3, 5, 8
 3,6,7,8,9,13
3, 4, 6, 6
1,4
2,  4, 6,7
 W. 9/13
#3 2.1
2.2
2.3
2.4
 3,7,11
2,5,9,11,17
2,3,7,8,10
4,6,8,10,12,15,22
 5,9,10
3,4,10,12,14, 21
1,4,5,6,9,15,16
2,5,9,13,16,17,20
 M. 9/25
#4 2.5
2.6
2.7
 2, 4, 6
3,4,7,10,11
1,3,5
 5,7,8
1,5,8,9, 12
2,6,8
 W. 10/4
#5 2.8
2.9
2.10
misc
 3, 4, 6, 8, 10
2, 4, 8
3, 9
4, 6, 10, 11
 2, 5, 7, 9, 11
3, 6, 7
6, 8, 10
5, 7, 8, 12
 F. 10/13
#6 3.1
3.2
3.3
3.4
 2
3,7,14,17
2,3,6,11,14,15
5,6,9
 1,3
1,4,8,13,15
1,4,5,8,10,12,13
7,10,11
 M 10/22
#7 3.5
3.6
Misc.
 3, 5
2,4
1, 2,7
 1, 2
1,5
3, 4, 5, 6
 W. 11/8
#8 4.1
4.2
4.3
4.6
 1,6, 8
2,4, 9
4, 6, 9
2,5,7
 2, 5, 9
1,5, 6
3,5,8
1,4,8
 M. 11/27
#9 5.5
5.6
5.7
6.1
6.2
6.3
 4, 8, 10
7
5
9, 12, 14
7,
7, 9, 13
 3, 9,
1,2
6
1, 2, 3, 10
6
4, 6, 8, 12
 F. 12/8
#10



#11



#12



 
Spring 2007. Math 731
HW #
 Sections
 Homework
 Practice Problems
 HW due date
1
 6.4
6.6
 2,6, 7,9, 13
2, 5, 6, 10, 15, 17,
 1, 3, 4, 8, 11, 14
3, 4, 7, 9, 11, 12, 16, 18
 Wed. 1/31
2
 not in the book
 Porblems at end of the web page!
Wed. 2/7
3
 6.7
6.8
 1
2, 5, 7, 12, 14
 2, 4
3, 6, 13
 Wed. 2/14

4
 10.1
10.2
10.3 		2, 6,8,13,14
6
4, 6, 9, 15, 19, 22, 26, 		3,4,9,11
7
2,5,8, 14, 17,20,29,30
Wed. 2/21
5
 10.4
10.5
 3, 5, 8
2, 4, 8, 12, 14, 16
 2, 6, 7
3, 5, 9, 13, 15,17
 Wed. 3/7
6
 10.6
10.7
 2, 4, 6,
2, 4, 6, 10, 12
 1, 7, 8, 9
1, 3, 6, 11, 13
 Wed. 3/14
7
 11.1
11.2
 1, 5, 10, 15
1,4, 7, 9,12,
3, 4, 6,9,11
2, 5,8,10, 14
 Wed.3/28
8
 11.3
11.4
 2,4,8,
2,8, 10, 12, 16
 1, 3, 7, 9
3, 9, 11, 14
 wed, 4/18
9
 12.1
12.2
12.7
 1,6, 10, 12
1, 5,
1,4, 6, 11, 15, 19
 3,7,8,11
3,6
2, 3, 5, 7, 8, 16, 17
Wed. 4/25
10
 13.1
13.2
13.3
13.6
 3
1,3,4,5
1, 3, 8, 12
9,10
 4
2,3
2,5,9,13
11,


W. 5/2

Homework Grading Rubric
Add-Drop, and Exam Policies
 Procedures on dealing disruptive students in class
Student Code of conduct
Statement of Student Classroom Conduct


Hw #2. 

1. Let R be the field of all real numbers and n>1 be an postive integer with a . Let GLn(R) be the group of all real nxn matrices and Bn(R)and Un(R)be, respectively, the subgroup of all  invertible upper triangular matrices and the subgroup of invertible upper triangular matrices with 1's on the diagonals
in GLn(R).

(a) Compute the derived series of GLn(R) and prove that GLn(R) is not solvable.

(b) Find a subnormal series  with abelian subquotients for Bn(R) to prove that Bn(R) is solvable.

(c) Compute the lower central series of  Bn(R) to show that  Bn(R) is not nilpotent.

(d) Compute the lower central series of Un(R) to show that Un(R) is nilpotent.

(e) Compute the quotient group Bn(R)/Un(R) and show that it is abelian. Thus both Bn(R)/Un(R) and Un(R) are nilpotent but Bn(R) is not nilpotent.


2. Prove  any group  of  order  pq with p and q being prime numbers is solvable.