Question

(a) Show that GLn(F) is finite if and only if F is finite. (b) Show that...

  1. (a) Show that GLn(F) is finite if and only if F is finite. (b) Show that if |F| = q then |GLn(F)| ≤ q^n2.

    (c) Show that GLn(F) is nonabelian if n > 2 (regardless of the field F.)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let p(x) be an irreducible polynomial of degree n over a finite field K. Show that...
Let p(x) be an irreducible polynomial of degree n over a finite field K. Show that its Galois group over K is cyclic of order n and then show how the Galois group of x3 − 1 over Q is cyclic of order 2.
4) Let F be a finite field. Prove that there exists an integer n ≥ 1,...
4) Let F be a finite field. Prove that there exists an integer n ≥ 1, such that n.1F = 0F . Show further that the smallest positive integer with this property is a prime number.
show that F={a+bi |a,b ∈ Q} is a field
show that F={a+bi |a,b ∈ Q} is a field
(Modern Algebra) Show that every finite subgroup of the multiplicative group of a field is cyclical....
(Modern Algebra) Show that every finite subgroup of the multiplicative group of a field is cyclical. (Hint: consider m as the order of the finite subgroup and analyze the roots of the polynomial (x ^ m) - 1 in field F)
Prove that if F is a field and K = FG for a finite group G...
Prove that if F is a field and K = FG for a finite group G of automorphisms of F, then there are only finitely many subfields between F and K. Please help!
show that E is a finite open interval in R if and only if x +...
show that E is a finite open interval in R if and only if x + E is one. Then prove |E| = |x + E|.
Let F be the set of all finite languages over alphabet {0, 1}. Show that F...
Let F be the set of all finite languages over alphabet {0, 1}. Show that F is countable
Prove that for any positive integer n, a field F can have at most a finite...
Prove that for any positive integer n, a field F can have at most a finite number of elements of multiplicative order at most n.
Show that any dihedral group is isomorphic to a subgroup of GLn(R). (Be as precise as...
Show that any dihedral group is isomorphic to a subgroup of GLn(R). (Be as precise as possible, giving an explicit map between generators r, s of D2n and certain 2 × 2 matrices.)
Let A be a finite set and let f be a surjection from A to itself....
Let A be a finite set and let f be a surjection from A to itself. Show that f is an injection. Use Theorem 1, 2 and corollary 1. Theorem 1 : Let B be a finite set and let f be a function on B. Then f has a right inverse. In other words, there is a function g: A->B, where A=f[B], such that for each x in A, we have f(g(x)) = x. Theorem 2: A right inverse...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT