Mathematics Assignment | Custom Assignment Help

All questions on Assignment 3 are based on the material covered in Weeks 5 and 6. See the bottom

of the last page for a breakdown of the marks for this assignment.

Q 1. (a) Write down the set U14.

(b) Find the order of each element of U14 in the group (U14; ⊗14). Give the details of your calculations, but try to do as few calculations as you can, instead justifying your answers using

Chapter 6. You may find it convenient to give your final answer in table form.

(c) Is (U14; ⊗14) a cyclic group? Justify your answer.

(d) Write down all subgroups of (U14; ⊗14), and explain why there are no subgroups other than

these. You may use any of the results from Chapter 6 in your explanation.

Q 2. Let G be the group of symmetries (including flips) of the regular

octagon (8-gon) shown on the right. As usual, we regard the elements

of G as permutations of the set of vertex labels; thus, G 6 S8.

(a) Calculate the order of G using the Stabiliser-Orbit Theorem.

(b) Let µ denote the flipping symmetry of the 8-gon that takes the

vertex 1 to the vertex 6. Write the permutation µ in cycle form

(as a cycle or a product of disjoint cycles).(c) What is the order of µ in the group G?

(d) Does µ stabilise any vertical  Get mathematics assignment homework help today