field

I have a question that I don't know the answer to.

Let F be a field. I showed that SL2(F) defined to be the matrix
(a b
c d) where a,b,c,d are in F and ad-bc=1 is a group.

I already proved that.

However, the question goes on to ask,
If F has q elements, how many elements are in the group SL2(F)?
I don't know the answer.

Quote:

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Originally Posted by PvtBillPilgrim

I have a question that I don't know the answer to.

Let F be a field. I showed that SL2(F) defined to be the matrix
(a b
c d) where a,b,c,d are in F and ad-bc=1 is a group.

I already proved that.

However, the question goes on to ask,
If F has q elements, how many elements are in the group SL2(F)?
I don't know the answer.

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Think about it, what you actually want to know are the elements that are units. Our good friend rgep has given an exlanation here.

So it would just be:
((q^n)-1)*((q^n)-(q^n-1)) where n=2 in this case?

Thus, ((q^2)-1)*((q^2)-(q))

Quote:

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Originally Posted by PvtBillPilgrim

So it would just be:
((q^n)-1)*((q^n)-(q^n-1)) where n=2 in this case?

Thus, ((q^2)-1)*((q^2)-(q))

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No!


Or if you want to be cool :cool:

I don't know the dimension?