Order of a general linear group over a finite field

Choosing linearly independent columns successively gives

∣ G L_{n} (F_{q}) ∣ = (q^{n} - 1) (q^{n} - q) \dots (q^{n} - q^{n - 1}) = q^{n (n - 1) /2} \prod_{k = 1}^{n} (q^{k} - 1) .

 Ancestors (7)