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# Stabilisers and fixed set watch

1. Hi, just need to see if my answers are correct for the below as I keep getting confused with this topic.

Question

The following equation defines a group action of (R*, x) on the plane R^2

C ^ (x,y) = (cx,y) ^ is 'wedge'

Determine the stabilisers of (1,0) and (0,1)

Also, find the fixed set Fix(3).

stab(1,0) = R*
stab (0,1) = R*

Fix(3) = (3x,y) = (0,y) the y-axis
2. (Original post by jojo55)
Hi, just need to see if my answers are correct for the below as I keep getting confused with this topic.

Question

The following equation defines a group action of (R*, x) on the plane R^2

C ^ (x,y) = (cx,y) ^ is 'wedge'

Determine the stabilisers of (1,0) and (0,1)

Also, find the fixed set Fix(3).

stab(1,0) = R*
stab (0,1) = R*

Fix(3) = (3x,y) = (0,y) the y-axis
I don't agree with your first answer - think again about which elements of R* fix (1,0). The last two answers look good to me though.
3. (Original post by Mark13)
I don't agree with your first answer - think again about which elements of R* fix (1,0). The last two answers look good to me though.
Thanks for clarifying. I'm not too sure still about the first one then but I'll keep at it.
4. (Original post by Mark13)
I don't agree with your first answer - think again about which elements of R* fix (1,0). The last two answers look good to me though.
is it {1}?
5. (Original post by jojo55)
is it {1}?
Yep
6. (Original post by Mark13)
Yep
Woo!

Thanks
7. (Original post by jojo55)

Fix(3) = (3x,y) = (0,y) the y-axis
Just to add to what has already been said, what you have written here makes no sense:

Fix(3) is the set of points in the plane (x,y) such that 3 ^ (x,y) = (x,y).

So Fix(3) isn't equal to (3x,y) it is equal to the set of (x,y) such that (3x,y)=(x,y) which is equal to the set of all points (0,y).

This might seem pedantic but the more you write things that don't make any grammatical sense when you try to answer questions - the more you will just confuse yourself in future. It doesn't take much longer to write

Fix(3) = {(x,y) e R^2 |3x=x} = {(0,y)|y e R^2}

than what you wrote but at least it requires you to think about what type of objects you are dealing with.
8. (Original post by Mark85)
Just to add to what has already been said, what you have written here makes no sense:

Fix(3) is the set of points in the plane (x,y) such that 3 ^ (x,y) = (x,y).

So Fix(3) isn't equal to (3x,y) it is equal to the set of (x,y) such that (3x,y)=(x,y) which is equal to the set of all points (0,y).

This might seem pedantic but the more you write things that don't make any grammatical sense when you try to answer questions - the more you will just confuse yourself in future. It doesn't take much longer to write

Fix(3) = {(x,y) e R^2 |3x=x} = {(0,y)|y e R^2}

than what you wrote but at least it requires you to think about what type of objects you are dealing with.
Thanks. I get confused when trying to explain it as I don't fully understand it myself.

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