Mathematics Assignment | Custom Assignment Help

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

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

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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

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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

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