Assignment 4
PMAT 315 - Abstract Algebra
March 3
Reading: Sections 2.5, 2.6, 2.8 begin 2.9.
Written Excercises
The solutions to these problems are due in class on Wednesday, March 17.
- Section 2.5 p. 124 #3, 9, 14, 38
- Section 2.6 p. 136 # 3, 6 (ST=such that), 15, 23, 31, 34
- Section 2.8 p. 152 # 3, 13*, 16
* The excercise as stated in 13(a) is INCORRECT. Please instead prove that if
G is generated by a set X, then a subgroup H of G is normal if and only if xHx^{-1} AND x^{-1}Hx are both contained in H. I will give a bonus of between 1 and 3 points on the next quiz for a counterexample to the original statement.
Additional Recommended Excercises
These problems are recommended to help you learn the concepts. In many of these problems, you need not do all of the parts in order to master the concept. Use your judgement. You do not need to turn in these problems.
- Section 2.5, p. 124 #1, 5, 8, 11, 12, 21, 31, 37
- Section 2.6 p. 136 # 1, 2, 5, 9, 12, 24, 32
- Section 2.8 p. 152 # 3, 13, 16