**5520, Fall 2004: Review Sheet for Final
Exam**

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 material.