411 Midterm 1 Review Questions
Paul Hacking
October 12, 2011
(1) Give the denition of a group G.
(2) Suppose G is a group and x, y, z, w are elements of G satisfying the
equation xyz 1 w = e. Solve for y.
(3) In each of the following cases, determine whet
Math 411 Homework 2
Due: Tuesday, Jun-28-2011
Answers to the following should be turned in by the end of class on the above date. Write
your name on the assignment and make sure all pages are secured if it spans multiple
pages. This assignment is worth a
Math 411 Homework 3
Due: Thursday, Jul-7-2011
Answers to the following should be turned in by the end of class on the above date. Write
your name on the assignment and make sure all pages are secured if it spans multiple
pages. This assignment is worth a
Math 411 Homework 1
Due: Tuesday, Jun-21-2011
Answers to the following should be turned in by the end of class on the above date. Write
your name on the assignment and make sure all pages are secured if it spans multiple
pages. This assignment is worth a
411 Final Review Questions
Paul Hacking
December 2, 2011
(1) Let G and G be groups. Recall that a homomorphism from G to G
is a function : G G such that (ab) = (a)(b) for all a, b
G. Which of the following functions are homomorphisms? If is a
homomorphis
Math 411 Midterm 1, Thursday 10/13/11, 7PM-8:30PM.
Instructions: Exam time is 90 mins. There are 6 questions for a total of 70
points. Calculators, notes, and textbook are not allowed. Justify all your
answers carefully. If you use a result proved in the
411 Midterm 2 Review Questions
Paul Hacking
November 10, 2011
(1) Recall that the symmetric group Sn is the group of permutations of the
set cfw_1, 2, . . . , n, with operation given by composition of functions. Let
S8 be the permutation
=
1 2 3 4 5 6 7
Math 411 Midterm 2, Thursday 11/17/11, 7PM-8:30PM.
Instructions: Exam time is 90 mins. There are 7 questions for a total of 75
points. Calculators, notes, and textbook are not allowed. Justify all your
answers carefully. If you use a result proved in the
Math 411 Homework 4
Due: Wednesday, Jul-13-2011
Answers to the following should be turned in by the end of class on the above date. Write
your name on the assignment and make sure all pages are secured if it spans multiple
pages. This assignment is worth