# UCLA Abstract Algebra Actions on The Dihedral Group & Orbit Stabilizer Theorem Exercise

Description

Requisite information is provided in the attached image.Requirements: Everything must be written out clearly and all theorems utilized MUST be cited.

1 attachmentsSlide 1 of 1attachment_1attachment_1

Unformatted Attachment Preview

We are going to use the standard action to make a different action of D12 on a set
with five elements. Consider the picture
5
6
4
1
3
2
Let A = {1,3,5} be the vertices of the red triangle, let B = {2,4,6} be the vertices
of the blue triangle, and let X = {1,4}, Y = {2,5), and Z = {3,6} be the vertices
of the three green diagonals. The action of D12 on the set of vertices {1,2,3,4,5,6}
induces an action of D12 on the set {A, B, X, Y, Z}.
(A) Compute r· A, r.B, r.X, r. Y, and r. Z. Do the same with r replaced
by s.
(B) What is the orbit of A? What is the orbit of X?
(C) What is the stabilizer of X? Hint: you can find the order of the stabilizer
quickly using the orbit stabilizer theorem.
(D) Write down the permutations 0, and o, in Ss corresponding to the
elements res e D12.

Purchase answer to see full
attachment

Tags:
Permutations

Abstract Algebra

Algebra Actions

The Dihedral Group

Orbit Stabilizer Theorem

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

## Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.

Peter M.
So far so good! It's safe and legit. My paper was finished on time...very excited!
Sean O.N.
Experience was easy, prompt and timely. Awesome first experience with a site like this. Worked out well.Thank you.
Angela M.J.
Good easy. I like the bidding because you can choose the writer and read reviews from other students
Lee Y.
My writer had to change some ideas that she misunderstood. She was really nice and kind.
Kelvin J.
I have used other writing websites and this by far as been way better thus far! =)
Antony B.
I received an, "A". Definitely will reach out to her again and I highly recommend her. Thank you very much.