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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2007 • Question 1

Question

Math 6310 • Algebra Fall 2007 • Question 1

Let \(\mathbb {F}_q\) be a finite field of order \(q\). Compute the order of \(GL_n(\mathbb {F}_q)\), the group of invertible \(n\times n\) matrices with coefficients in \(\mathbb {F}_q\).

Raw LaTeX

Let \(\mathbb{F}_q\) be a finite field of order \(q\). Compute the order of
\(GL_n(\mathbb{F}_q)\), the group of invertible \(n\times n\) matrices with coefficients in
\(\mathbb{F}_q\).

Topic Tags

Finite Fields Finite Group Theory Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization