This preview shows page 1. Sign up to view the full content.
Math 5125
Monday, August 22
First Homework
Due 9:05 a.m., Friday August 26
1. Section 3.2, Exercise 8 on page 95.
(2 points)
2. Let
A
be a normal abelian subgroup of the group
G
and let
H
≤
G
. Suppose
AH
=
G
.
Prove that
A
∩
H
±
G
. Hint: if
g
∈
G
, write
g
=
ah
and then show
a
(
A
∩
H
)
a

1
=
A
∩
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: H = h ( A ∩ H ) h1 . (2 points) 3. Let H ≤ G be ﬁnite groups and let θ : G → G 1 be a group homomorphism. Prove that  θ ( G ) : θ ( H )  divides  G : H  . (3 points) (3 problems, 7 points altogether)...
View
Full
Document
This note was uploaded on 01/02/2012 for the course MATH 5125 taught by Professor Palinnell during the Fall '07 term at Virginia Tech.
 Fall '07
 PALinnell
 Math, Algebra

Click to edit the document details