# Embedding of general linear groups

Can we embedd $GL(2n,q)$ into $GL(n,q^2)$ for $n\in \mathbb{N}$ and $q=p^m$, $p$ a prime? If yes, how?

-
Can you embed $GL_2(p)$ into $GL_1(p^2)$? Hint: What are their respective orders? Always think about the simplest non-trivial example before asking a general question. –  Alex B. Mar 29 '11 at 6:51
If you had instead asked whether we could embed ${\rm GL}(n,q^2)$ into ${\rm GL}(2n,q)$, then the answer would have been different. –  Derek Holt Mar 29 '11 at 11:46
did you not just completely change the question? Please do not do that. –  Mariano Suárez-Alvarez Mar 30 '11 at 4:21