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 havea natural product operation, which makes RP' a group-in fact, it is the groupSO(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 normalsubgroup.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'.2.3The groups SU(2) and SO(3)

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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,...

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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)

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