Fall 2011, Math 405/505

Class: MWF 1:40-2:30, MG 124

Instructor: Dr. Zach Teitler
Office: MG 220B
Phone: 208-426-1086
E-mail: zteitler@boisestate.edu
Office hours: TBA and by appointment

Syllabus: pdf, html

Textbook: Abstract Algebra: Theory and Applications by Tom Judson
Download here: AATA (with hyperlinks) or AATA (without hyperlinks)
The textbook will be for sale in the campus bookstore.
Please do not purchase the 2009 edition of the book from Amazon.
The author has made a 2011 edition of the book, which is available on the textbook web site and also from Amazon. You are welcome to use that instead of the version in the campus bookstore. If you have already bought a copy of the book from the campus bookstore, you do NOT need to switch to the author's 2011 edition as it has only very minor differences from the bookstore version.
Click here to download the differences between the bookstore version and the author's 2011 edition: pdf, html

Important dates:

An illustration of the Third Isomorphism Theorem.

Web sites with Java applets to explore dihedral groups interactively:

Some short articles:

Some surprising elementary open questions:

Useful websites:

Homework:
Assignment Assigned problems Due date
1 Ch. 3 # 5, 10, 30 + 3 more Wed, 8/31/11
2 Ch. 4 # 12, 23, 34, 41 + 3 more Wed, 9/7/11
Fri, 9/9/11
3 Ch. 4 # 31
Ch. 5 # 2, 3, 14, 27 + 2 more
Prove: If H, K < G and H ∪ K < G, then H ⊂ K or H ⊃ K
Prove: If A_1 < A_2 < ... < G is a nested sequence of subgroups of G then the union of the A_i is a subgroup of G
Wed, 9/21/11
4 Ch. 6 # 5, 8, 17, 19. Students in Math 505: also, Ch. 6 # 21. Wed, 9/28/11
5 Ch. 9 # 9, 16, 35 + 3 more chosen out of the following:
  • Students in Math 505 choose from 8, 11, 14, 20, 22, 29, 31, 36, 37, 38+39, 40, 41, 42, 43, 52, 53, 54.
  • Students in Math 405 choose from 3, 8, 11, 14, 20, 21, 22, 29, 31, 32 (first part), 36, 37, 38+39, 40, 41, 42, 43, 45, 52, 53, 54.
Wed, 10/19/11
6 Ch. 10, 5 problems of your choice Wed, 10/26/11
7 Ch. 11, # 2, 5, 7, 14
One out of Ch. 11 #12, 16, 17, 18 (your choice)
Give an example of a group G, subgroup K, and normal subgroup N, such that the intersection K ∩ N is not a normal subgroup of N.
Prove: If A_1 < A_2 < ... < G is a nested sequence of subgroups of G such that G = ∪ A_i and each A_i is simple, then G is simple.
Wed, 11/2/11
Fri, 11/4/11
8 Ch. 13 # 1, 3, 6, 12, 15, 16, + 1 more chosen out of #7 (hard!), 8, 10, 11, 14, 17
Students in Math 505: Turn in a brief written description of your presentation.
Wed, 11/16/11
9 Two out of Ch. 14 # 2+3, 4, 5 (your choice)
Two out of Ch. 14 # 22, 23, 24 (your choice)
A) Let X be the set with 27 elements X = {(i,j,k), 1 ≤ i,j,k ≤ 3}. Then G = S_3 acts on X by σ(i,j,k) = (σ(i),σ(j),σ(k)). For each x in X find the stabilizer of x and the orbit of x.
Students in 505 also do the following:
B) Show: If H is a subgroup of G of index n, then there exists a normal subgroup K of G, contained in H, whose index divides n! (n factorial). (Hint: Consider the permutation representation associated to the action of G on G/H.)
C) Show: If G is a finite p-group then every subgroup of index p is normal. (Hint: Use (B).)
Wed, 11/30/11

zteitler@boisestate.edu


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