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
I am reading Dummit and Foote Section 3.1: Quotient Groups and Homomorphisms.
Exercise 17 in Section 3.1 (page 87) reads as follows:
-------------------------------------------------------------------------------------------------------------
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
------------------------------------------------------------------------------------------------------------------
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
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