George T. Walker Hall, Room 3 - 34
For each homework set, complete all of the exercises but only hand in those in bold.
| Assignment | Problems |
|---|---|
| 1 | 1.1.1, 1.1.2, 1.1.6, 1.1.9, 1.1.11, 1.1.12, 1.1.13, 1.1.14, 1.1.15, 1.1.16, 1.1.18, 1.1.20, 1.1.25 [Hint: Use 1.1.18], 1.1.31 [Hint: pair every element x with its inverse.], 1.2.1, 1.2.10 |
| 2 | 1.3.1, 1.3.2, 1.3.3, 1.3.9, 1.3.14 [Hint: Show that a ~b iff b = \sigma^i(a) is an equivalence relation. What is the equivalence class of a?], 1.6.1, 1.6.2, 1.6.4, 1.6.5, 1.6.7, 1.6.8, 1.6.17, 1.6.18 |
| 3 | 1.6.11, 1.6.21, 1.7.3, 1.7.16, 1.7.17, 2.1.1, 2.1.2, 2.1.8, 2.1.10, 2.1.11 |
| 4 | 2.2.3, 2.2.4, 2.2.5, 2.2.6, 2.2.7, 2.3.1, 2.3.10, 2.3.11, 2.3.12, 2.4.14, 2.4.15 |
| 5 | 2.3.25, 2.3.26, 3.1.1, 3.1.6, 3.1.7, 3.1.8, 3.1.9 |
| 6 | 3.1.4, 3.1.5, 3.1.18, 3.1.19, 3.1.22, 3.1.24, 3.1.36, 3.1.42 |
| 7 | 3.2.4, 3.2.6, 3.2.8, 3.2.14, 3.3.5, 3.3.6 |
| 8 | 3.4.2, 3.4.3, 3.5.2, 3.5.3, 3.5.4, 3.5.6, 3.5.7, 3.5.11, 3.5.14 [Hint: Use the Lagrange's Theorem and the lattice on p. 111], 4.2.1, 4.2.2, 4.2.3, 4.2.4, 4.2.7 [Hint: Use the Orbit-Stabilizer Theorem] |
| 9 | 4.3.5, 4.5.14, 4.5.15, 4.5.17, 5.2.1, 5.2.2, 5.2.3, 5.2.4 |
| 10 | 4.5.26, 4.5.27, 4.5.30, Prove by induction that a p-group is solvable., 7.1.1, 7.1.2, 7.1.3, 7.1.5, 7.1.6, 7.1.7, 7.1.11, 7.1.15, 7.1.16, 7.1.28, 7.1.29, 7.1.30 |
| 11 | 7.2.1, 7.3.1, 7.3.4, 7.3.6, 7.3.11, 7.3.12, 7.4.4, 7.4.5, 7.4.7, 7.4.8 |