Summary: Math 3130 Midterm: Due Wednesday October 22 in Class
Remember to show your work!
Directions This is a take home, open notes test. There are eight problems on the test. You must
answer carefully and completely any five of the problems. You answer must be your own; you
are free to discuss problems with other students but must write up your own answers. Excessive
similarity of answers will be noted and dealt with appropriately.
Problem 1 Find all possible cycle types in S5 and say how many permutations there are with
each cycle type.
Problem 2 Compute GCD(54, 45) = 54x + 45y using the Euclidean algorithm and solving for
x and y by back substitution through the Euclidean algorithm.
Problem 3 Let A be a group with two elements and so that A consists of all possible products
in any order of and . If and satisfy the following relations:
Prove the following identities hold in A.
(i) = 2
, (ii) = 2