Hi, i am really struggling with this question. There seems to be lots of different methods and it's very confusing! Any help would be greatly appreciated!
Consider the field Fp with p elements. Determine the number of elements in the following groups:
So far I have (p^n -1)(p^n -p)...(p^n -p^(n-1)) and now I am stuck as my lectures are rather unhelpful!
Thanks in advance, Katie
No nullspace and stuff: we're in group theory here and you ought to know what the kernel of a group homomorphism is, otherwise this question is out of your league, at least for now.
The special group is just the subgroup of all the invertible matrices whose determinant is 1...
Now check again my first message to you and use the first isomorphism theorem for group homomorphisms...and perhaps Lagrange's Theorem, too.