# UCLA Abstract Algebra Transitive and Stabilizer of D12 Set of Vertices Exercise

Description

Part 1: Prove that the action is transitivePart 2: Compute the stabilizer of the vertex
Both parts MUST be written out rigorously with all theorems used cited.

1 attachmentsSlide 1 of 1attachment_1attachment_1

Unformatted Attachment Preview

In this question you will think about D12. Remember that we have the standard
presentation
D12 = (r, s|96 = 52 = 1, rs = sr=1)
Consider the usual action of D12 on the regular hexagon, as pictured below:
5
6
4
1
3
2
As we discussed in lecture, we can think of this as an action of D12 on the set of vertices
{1,2,3,4,5,6}. Specifically, in terms of the induced permutation representation, the
rotation r corresponds to the permuation (123456) ES6, and the reflection s corresponds
to (26)(35) E \$6.

attachment

Tags:
Abstract Algebra

HEXAGON

Figure vertices

Vertex stabilizer

Transitive action

permutation representation

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.