Math 336
Dr. Karlof
NAME
Quiz 6
This quiz is due Tuesday, May 22, before class or in class.
1. Let : G G be an automorphism. Prove: H = cfw_x G : (x) = x is a subgroup of G.
2. Let G = S3 Z4 . Let K = cfw_(1), 0), (123), 0), (132), 0), (1), 2), (123), 2),
1. Suppose g G and | g | =24. Find
|g6|
and g 15 .
2. Consider the group G = cfw_s, t, u, x, y, z defined by the following table
a. What is the identity of G?
b. What is the inverse of t? of z?
c. Find Z (G)
d. Find z
e. Find s
s
t
u
x
y
z
s
t
u
x
y z
x