Math 5331 Schedule/Homework
Date  Topic  Homework  Due date  Reading assignment 
Tuesday 3/4  Group actions 
Study the
examples given in class. Study the actions given on p.43 (#4), p. 52 (#1, 2) 
pp. 4145, 5153  
Thursday 3/6  Transitive group actions  Study the actions given on p.113 (#2, 3, 4) and on p.115 (# 4, 5).  pp.112117  
Tuesday 3/11  Cayley's Theorem  Do problems # 4, 5, 6, 13, 14, 15, 16, 18 on pages 4445 
3/27 HW # 7 
pp. 118121 
Thursday 3/13  The class equation  Do problem # 8 on page 53. Handout II on Groups 
4/1 HW # 8 
pp.122129 
March 1721 
Spring Break 
Spring Break 
Spring Break 

Tuesday 3/25  No class. Work on Handout II.  pp. 133144.  
Thursday 3/27  The Sylow Theorems 
Study
the following: Examples on page 144 Propositions 21 and 23 Corollary 22 on page 145. 
pp. 144146  
Tuesday 4/1 
The
Sylow Theorems Take home test (Test # 3 given out.) Due Tuesday April 8. 
Handout III on Groups. 
pp. 152165  
Thursday 4/3 
Direct
product. Finitely generated abelian groups. 
p. 147 # 13, 18, 30 pp. 15615 7# 1, 18 ac pp.165166 # 1 a, b; 2 ac; 3 ac; 4 
4/15 HW # 9 
pp. 188194 
Tuesday 4/8 
Abelian
groups. Nilpotent groups. 
Handout IV on Nilpotent Groups  pp. 194199  
Thursday 4/10  Solvable groups 
Problem # 8 on page 198. Handout V on Solvable groups. pp. 173174 # 1, 2, 4, 7, 10 
4/22 HW # 10 
pp. 223230 
Tuesday 4/15  Introduction to Rings  pp. 230231 # 1, 2, 3, 4, 7, 9, 11, 15, 21  
Thursday 4/17 
Ring
homomorphisms. Ideals 
p. 237
# 1 p.249 # 16, 18, 22, 24a, 27, 28 

Tuesday 4/22  Review  
Thursday 4/24  Test # 4  
Tuesday 4/29  
Thursday 5/1  
Tuesday 5/6 
Final Exam 11:00 am1:30 pm 
Date  Topic  Homework  Due date  Reading assignment 
Thursday 2/7  Cosets  
Tuesday 2/12  Normality. Quotient groups. 
Prove
the following: 1. Corollaries to Lagrange's theorem. 2. Prove the equivalent definitions of normal subgroup. 3. If , then . 4. If A and B are normal subgroups of G, then their intersection is also normal in G. 5. If N is a normal subgroup of G and , then . 
2/21 HW # 4 
pp. 89100 
Thursday 2/14  The isomorphism theorems 
1. pp.
8588 # 3, 4, 22, 24, 30, 31, 36 2. pp. 95 # 1, 4, 5, 8 3. Study the statements and proofs of Propositions 13, 14, and 15 on pages 9394. 4. Study the proof of the Proposition given in class. 
2/21 HW # 4 
pp. 101105 
Tuesday 2/19  Simple groups  Handout I on Groups ALL 
2/26 HW # 5 
pp. 106110 
Thursday 2/21  Alternating groups 
1. Show that if G is a simple group, then any homomorphic
image of G is either isomorphic to G or of order one. 2. p111 # 1, 2, 3 
3/6 HW # 6 

Tuesday 2/26  Examples  
Thursday 2/28  Test # 2 
Date  Topic  Homework  Due date  Reading assignment 
Tuesday 1/15  Introduction to groups: Definitions and Examples 

1/24 HW # 1 
pp 1625; 2932 
Thursday 1/17 
Properties of groups. Dihedral and Symmetric groups 

1/24 HW # 1 
pp 3639; 4648 
Tuesday 1/22  Homomorphisms and isomorphisms 

1/31 HW # 2 
pp 4951, 5456 
Thursday 1/24 
Normalizers and centralizers. Cyclic groups 

1/31 HW # 2 
pp 5664 
Tuesday 1/29  Generators 

2/7 HW # 3 
pp 6671 
Thursday 1/31  Lattices of subgroups  p. 71 # 2 (a, c, d), 9 (a, b)  2/7 HW # 3 

Tuesday 2/5  Test # 1 