 
Summary: Math 3130 Midterm: Due Wednesday October 21 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 Give the Cayley table of (Z
36, ·) and determine the order of each element.
Problem 2 Prove that
(P({a, b, c}), )
is a group, give the Cayley table, determine if the group is commutative, and give the order of
each element.
Problem 3 Compute GCD(56, 91) = 91x + 56y using the Euclidean algorithm and solving for
x and y by back substitution through the Euclidean algorithm.
Problem 4 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:
3
= 3
= ()2
= e
