Algebra

**peteryellow** · Jan 31st 2009, 05:43 AM

Here GL(n,K) is the general linear group of degree n over a field K.
Show that GL(n,K) is a finite group if and only if K is a finite field.

**clic-clac** · Jan 31st 2009, 08:47 AM

$k$ a field and $n$ a positive integer.

$\forall x\in k,\ x.I_n\in GL(n,k)\Rightarrow (GL(n,k)\ \text{finite}\Rightarrow k\ \text{finite})$
$k\ \text{finite}\Rightarrow k^{n\times n} \text{finite}\Rightarrow GL(n,k)\ \text{finite}$

Thread: Algebra

LinkBack

Thread Tools

Display

Algebra

Similar Math Help Forum Discussions

Is a countable union/intersection of sigma-algebra also a sigma-algebra?

Is linear algebra considered to be a type of abstract algebra?

Algebra or Algebra 2 Equation Help Please?

terminology about ring/algebra in abstract algebra and measure theory

algebra 2 help

Search Tags