### Homework for Abstract Algebra I

Math 171, Fall 2017, Harvey Mudd College
Prof. Orrison

Unless stated otherwise, Monday homework is due at the beginning of class, and Thursday homework is due outside my office by 5:00 PM. Also, please keep in mind that the exercises at the end of each reading assignment are considered part of the reading assignment. You will find many important ideas, examples, and techniques introduced in the exercises.

1. Due Mon. 9/4: Groups

2. Due Thu. 9/7: Dihedral Groups
Problems — (1.2) 2, 3, 4, 5.
Rewrite Due 9/21.

3. Due Mon. 9/11: Symmetric Groups
Problems — (1.3) 1, 2, 10, 11.
Rewrite Due 9/25.

4. Due Thu. 9/14: Matrix Groups and the Quaternion Group
Problems — (1.4) 10, 11(a-b). (1.5) 1, 2.
Rewrite Due 9/28.

5. Due Mon. 9/18: Homomorphisms
Problems — (1.6) 13, 14, 16, 23.
Rewrite Due 10/2.

6. Due Thu. 9/21: Group Actions
Problems — (1.7) 4, 17, 18, 19.
Rewrite Due 10/5.

7. Due Mon. 9/25: Subgroups
Problems — (2.2) 4, 9, 10, 14.
Rewrite Due 10/9.
Note: This is the last assignment you will be able to rewrite and resubmit.

8. Due Mon. 10/9: Lattices of Subgroups
Problems — (2.5) 1, 4, 5, 8.

9. Due Thu. 10/12: Quotient Groups
Problems — (3.1) 40, 41, 42, 43.

10. Due Mon. 10/23: Cosets
Problems — (3.2) 4, 18, 19, 20.
Note: Make sure to read Exercises 9, 16, and 22, and think about how might you solve those problems.

11. Due Thu. 10/26: The Isomorphism Theorems
Problems — (3.3) 3, 4, 8, 9.

12. Due Mon. 10/30: Group Actions
Problems — (4.1) 2, 3. (4.2) 4, 8.

13. Due Thu. 11/2: More Group Actions
Problems — (4.3) 6, 23, 24, 25.

14. Due Thu. 11/9: Rings
Problems — (7.1) 7, 14, 15, 16.

15. Due Mon. 11/13: Important Examples
Problems — (7.2) 7, 9, 10, 13.

16. Due Thu. 11/16: Ring Homomorphisms and Quotient Rings
Problems — (7.3) 21, 26, 28, 29.

17. Due Mon. 11/20: Properties of Ideals