Math 120 Homework 1 Solution
13 April 2006
1.1.Problem 9
(a) (a + b 2)+(c + d 2) is dened to be (a + c)+(b + d) 2. If a, b, c, d Q,
then a + c, b + d are also in Q. Therefore + is a binary operation on G.
To prove (G, +) is a group, we need to check three
Math 120 Homework 3 Solution
27 April 2006
2.1 Problem 2
(a) (12)(23) = (123) is not a 2-cycle, so the set of 2-cycles is not closed
under products. Hence its not a subgroup.
(b) D2n can be viewed as a subgroup of S2n , with generator and relations
given
Math 120 Homework 4 Solution
May 4th 2006
1.7 Problem 4
a Let K be the kernel of the action. If g , h K , then for any x A
we have g (x) = h(x) = x. Therefore (gh)(x) = g (h(x) = g (x) = x
and g 1 x = x, so K is closed under product and inverse. Of course
Math 120 Homework 6 Solution
18 May 2006
Page 85. Problem 3
: G G/N
g gN
(g1 ) (g2 ) = g1 N g2 N = (g1 g2 )N = (g1 g2 ) = (g2 g1 ) = (g2 ) (g1 )
So G/N is an abelian group.
Example: Let G = S3 , N =< (123) >, then G is non-abelian. G/N
contains only two
Math 120 Homework 7 Solution
25 May 2006
page 101, questions 3
We have formula |HK | =
|HK | divides G.
|H |K |
.
|H K |
Because HK is a subgroup of G,
|H |K |
|H K |
=
|K |
|G|
|H |K |
divides |G|
divides
=p
|H K |
|H K |
|H |
Because we have shown befo
Math 120. Basic Algebra
Midterm - Practice Questions
Note: These problems are only intended to help you study. Questions based an any material covered in
class may appear on the actual test.
1. True or false?
(a) The set of all positive real numbers is a
Math 120. Basic Algebra
Final Exam - Practice Questions
Note: These problems are only intended to help you study. Questions based an any material covered in
class may appear on the actual test.
1. True or false?
(a) If G1 and G2 are commutative groups the
Math 51 - Winter 2011 - Midterm Exam II
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