I am having trouble understanding groups in my group theory class. I am not confident on how to approach the following question:
I know that y4
= u. So then,
g = xy4
= xu = x. Then
which is what I am trying to prove.
Now if i = 1 then,
g = xy. Then
= xy xy = x yx y = x xy-1
y = x2
y = u y-1
= 2. Then
y = u u = u since
y = u.
First question: Is the work I have completed so far correct?
Second question: Do I need to prove this in a case by case basis? That is, I would think that I would have to prove this for i = 1,2,3,4. Since I have already completed 1 and 4, I would have to do cases in which i = 2,3. Correct?
This may seem elementry, but like I stated above, my confidence in answering such questions is not great. And my understanding of the material is very weak.
Any comments, input, help is appreciated.