This assignment covers the rest of group theory for Math 531. We won't do any of Chapters 9,10,11 completely; we'll only do part of each.
The following problems give you practice with the concepts in these chapters. I have tried to pick an interesting collection of problems. Some are very easy, some hard; some may be done in class. You might first browse through the problems and see which you can do easily and which interest you. The majority will not be turned in. Some will turn up (perhaps varied a bit) on exams.
Note: there are answers to most odd-numbered problems in the back of the book.
I will ask you to hand in some of these problems for a grade later. I may also assign additional problems. Some of these problems may form the basis of in-class presentations.
Chapter 8
Read Chapter 8 of Gallian.
p. 162 #1,3,4,5,6,7,8,9,10,11,12,15,16,19,22,23,24,25,26,
30,31,33,35,37,42,46,47,53,54
Supplementary Problems for Chapters 5-8
p. 169 #1,2,6,8,14,15,20,35,49,50
Chapter 9
Read the material on normal subgroups in Chapter 9 of Gallian, pp. 172-173.
p. 186 #1,3,4,5,7,46,47,48,62
Chapter 10
Read the material on homomorphisms and the kernel in Chapter 10 of Gallian, but not the isomorphism theorems. That is, read pp. 194-200.
p. 205 #2,5,7,8,9,19,33,35,36
Chapter 11
Read Chapter 11 of Gallian, but concentrate only on the result, not on the proof. That is, read pp. 212-213.
p. 219 #1,2,5,10,15,16,32
Supplementary Problems for Chapters 9-11
p. 224 #1,3,4,6,15,16,27