Ok, let's take the and see how we could get it to look like So the 's are the same, no issue there. Try this for the in
which is in
I think you'll find that the other elements behave in a similar fashion. Can you finish from here?
The group has two generators with the relations . Let be the cyclic group generated by . Write down the four elements in . Write down the four elements in the left coset and the four elements in the right coset . Show that .
This is what I have so far.
Now I am supposed to show that and I cannot seem to manipulate the sets so they are equal. Thanks in advance for any help.