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?
Embedding of general linear groups
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group-theory
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6Can 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. – 2011-03-29
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0If 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. – 2011-03-29
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2did you not just completely change the question? Please do not do that. – 2011-03-30