Math 330-A: Quiz 1.5
Northwestern, Fall 2013
November 5, 2013
As I said in class, this is a replacement for the rst quiz, consisting of similar problems. Ill use
your score on this to make-up your rst quiz score. The solutions to the rst quiz are online,
Math 330-A: Quiz 2
Northwestern, Fall 2013
November 5, 2013
Name:
1. Find the left and right cosets of the subgroup H = cfw_id, (1234), (13)(24), (4321) of S4 determined
by the elements (123) and (23). Is H is a normal subgroup of S4 ?
2. Find the orders
Math 330-A: Quiz 3 Solutions
Northwestern University, Fall 2013
1. Determine whether each of the following polynomials are reducible or irreducible over Q. For
any which is reducible, factor it into a product of irreducible polynomials.
(a) 4x5 6x4 9x3 +
Math 330-A: Quiz 3
Northwestern, Fall 2013
November 26, 2013
Name:
1. Determine whether each of the following polynomials are reducible or irreducible over Q. For
any which is reducible, factor it into a product of irreducible polynomials.
(a) 4x5 6x4 9x3
Math 330-A: Quiz 2 Solutions
Northwestern University, Fall 2013
1. Find the left and right cosets of the subgroup H = cfw_id, (1234), (13)(24), (4321) of S4 determined
by the elements (123) and (23). Is H is a normal subgroup of S4 ?
Solution. We have
(12
Math 330-A: Quiz 1
Northwestern, Fall 2013
October 22, 2013
Name:
1. Determine the largest order an element of Z6 Z9 can have, and nd four elements of that order.
Note that this group has 54 elements, so you should nd a way to do this which avoids trying
Math 330-A: Quiz 1 Solutions
Northwestern University, Fall 2013
1. Determine the largest order an element of Z6 Z9 can have, and nd four elements of that order.
Note that this group has 54 elements, so you should nd a way to do this which avoids trying to
Math 330-A: Quiz 1.5 Solutions
Northwestern University, Fall 2013
1. Determine the largest order an element of Z2 Z3 Z4 can have, and nd all elements of that
order.
Solution. For an element (a, b, c) Z2 Z3 Z4 , the possible orders of a are 1, 2, the possi
Math 330-A: Final Exam, or How I Learned to Stop
Worrying and Love Galois Groups
The goal of our last meeting is to exhibit an explicit polynomial of degree 5 which is not
solvable by radicals, thereby showing that there does not exist an analog of the qu