- #1
wubie
Hello,
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
g2 = x2 = u
which is what I am trying to prove.
Now if i = 1 then,
g = xy. Then
g2 = xy xy = x yx y = x xy-1 y. Then
xx y-1y = x2 y-1y = u y-1y since
x2 = 2. Then
u y-1y = u u = u since
y-1y = 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.
Thankyou.
I am having trouble understanding groups in my group theory class. I am not confident on how to approach the following question:
Let D = D8 be dihedral of order 8 so
D = {u,y,y2,y3,x,xy,xy2,xy3}
where x2 = u, y4 = u, and yx = xy-1.
Let g = xyi for some integer i. Prove that g2 = u.
I know that y4 = u. So then,
g = xy4 = xu = x. Then
g2 = x2 = u
which is what I am trying to prove.
Now if i = 1 then,
g = xy. Then
g2 = xy xy = x yx y = x xy-1 y. Then
xx y-1y = x2 y-1y = u y-1y since
x2 = 2. Then
u y-1y = u u = u since
y-1y = 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.
Thankyou.