Quotient Groups - Dummit and Foote, Section 3.1, Exercise 17

I am reading Dummit and Foote Section 3.1: Quotient Groups and Homomorphisms.

Exercise 17 in Section 3.1 (page 87) reads as follows:

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Let G be the dihedral group od order 16.

and let be the quotient of generated by .

(a) Show that the order of is 8

(b) Exhibit each element of in the form

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I have a problem with part (b) in terms of how you express each element of in the form requested - indeed, I am not quite sure what is meant by "in the form "

My working of the basics of the problem was to put and generate the cosets of H as follows:

So the order of is 8

**BUT** - how do we express the above in the form and what does the form mean anyway?

Would appreciate some help.

Peter

Re: Quotient Groups - Dummit and Foote, Section 3.1, Exercise 17

By representing each of the elements in the form , they simply mean choosing a coset representative. One element from each distinct coset.

I.e., The coset would be represented by either or