2.2.5 Show that S' is not a normal subgroup of S'.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Question
100%

Need help with 2.2.5 highlighted for modern algebra please, Thankyou

of the antipodal point pairs {±q} on the 3-sphere S³. These pairs likewise have
a natural product operation, which makes RP' a group-in fact, it is the group
SO(3) of rotations of R’. We will show that RP' is not the same group as Sº,
because SO(3) is simple and S³ is not.
We can see right now that S3 is not simple, by finding a nontrivial normal
subgroup.
2.2.4 Show that {±1} is a normal subgroup of S³.
However, it turns out that {±1} is the only nontrivial normal subgroup of S'.
In particular, the subgroup S' that we found in Section 2.1 is not normal.
2.2.5 Show that S' is not a normal subgroup of S'.
2.3
The groups SU(2) and SO(3)
Transcribed Image Text:of the antipodal point pairs {±q} on the 3-sphere S³. These pairs likewise have a natural product operation, which makes RP' a group-in fact, it is the group SO(3) of rotations of R’. We will show that RP' is not the same group as Sº, because SO(3) is simple and S³ is not. We can see right now that S3 is not simple, by finding a nontrivial normal subgroup. 2.2.4 Show that {±1} is a normal subgroup of S³. However, it turns out that {±1} is the only nontrivial normal subgroup of S'. In particular, the subgroup S' that we found in Section 2.1 is not normal. 2.2.5 Show that S' is not a normal subgroup of S'. 2.3 The groups SU(2) and SO(3)
Expert Solution
Step 1

Algebra homework question answer, step 1, image 1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education