Dummit and Foote (D&F) Section 1.2 Dihedral Groups, exercise 1(b) reads as follows:

Compute the order of each of the elements of .

D&F give the following as one presentation of :

= < r,s | = = 1, rs = >

Following this notation I proceeded to compute r, s and sr and (among other elements) was going to determine the order of sr. I proceeded as follows:

Given the set-up mentioned for the square - see attached pages from D&F on the Dihedral Groups - i defined r and s as follows:

r =

s =

Thus

sr =

So from these permutations I calculated that

= = 1

BUT!! from the relations given by D&F we have = 1 and so we can proceed thus to find

= = 1. ????

Can anyone help?