Homework 2
September 2, 2005
Math 521
Direction: This homework is due on September 9, 2005. In order to receive full credit, answer each problem completely and must show all work.
1. Prove by induction that for every positive integer n, 1 + 2 + 3 + + n =
Homework 5
September 30, 2005
Math 521
Direction: This homework is due on October 7, 2005. In order to receive full credit, answer each problem completely and must show all work.
1. Let G be a group and let H be a subgroup of G. For any x G, define xHx-1
Key to Homework 1
August 26, 2005
Math 521
Direction: This homework is due on September 2, 2005. In order to receive full credit, answer each problem completely and must show all work.
1. For each value of n listed, nd all positive integers less than n an
Test 3
November 11, 2005
Math 521
Name
Student Number
Direction: You are required to complete this test within 50 minutes. (If needed,
an extra 40 minutes will be allowed.) In order to receive full credit, answer each
problem completely and must show all
Test 2
October 14, 2005
Name
Math 521
Student Number
Direction: You are required to complete this test within 50 minutes. In order to receive full credit, answer each problem completely and must show all work. Good Luck!
1. (13 points) Determine the order
Test 1
September 16, 2005
Name
Math 521
Student Number
Direction: You are required to complete this test within 50 minutes. In order to receive full credit, answer each problem completely and must show all work. Good Luck!
1. (13 points) Prove by the meth
Homework 9
November 4, 2005
Math 521
Direction: This homework is due on November 11, 2005. In order to receive full
credit, answer each problem completely and must show all work.
1. Let H = cfw_0, 3, 6, 9, . be a subgroup of the additive group of integers
Homework 6
October 7, 2005
Math 521
Direction: This homework is due on October 14, 2005. In order to receive full credit, answer each problem completely and must show all work.
1. 1 1
For the following permutations = 2 6 3 3 4 4 5 5 6 8 7 2 8 7
1 3
2 6
3
Homework 4
September 23, 2005
Math 521
Direction: This homework is due on September 30, 2005. In order to receive full credit, answer each problem completely and must show all work.
1. Prove that in any group, an element and its inverse have the same orde
Homework 3
September 9, 2005
Math 521
Direction: This homework is due on September 16, 2005. In order to receive full credit,
answer each problem completely and must show all work.
1. With picture and words, describe each symmetry in D3 (the set of symmet
Homework 7
October 21, 2005
Math 521
Direction: This homework is due on October 28, 2005. In order to receive full credit, answer each problem completely and must show all work.
1. Consider the group G = cfw_1, i, -1, -i under multiplication. For an arbit