5520, Fall 2004: Review Sheet for Final
The test will be in roughly
the same format as the midterm: there will be two parts, one on theory
and one on
computation. Each part will contain 4 or 5 problems, and you will
have to do two or three of them. The exam will focus on Chapters
7-11 and 24-25; it will be comprehensive only in the sense that you
must be familiar with Chapters 1-6 in order to understand the later
chapters. Go over the homework problems assigned from these
chapters, and do other similar ones from the book for extra review.
The most important chapters are 7, 9, and 10: know their main
theorems. You should be comfortable with external direct products
as covered in Chapter 8, but they are not as central as the material of
7, 9, and 10. On a related note, you should know the version of
Theorem 9.6 proven in class, on the "internal direct products" of two
subgroups of a given group.
There will probably be one problem on Chapter 11. You should know
the main theorem of this chapter, and also how to count the number of
elements of a given order in a finite abelian group.
There will probably be two problems on Chapters 24 and 25, one
theoretical and one computational. Know the Sylow theorems and
how to apply them. Theorem 24.6 on pq groups is often
useful. The final problem set gives plenty of review for this