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.

Purchase answer to see full
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.