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Math Help - Algebra

  1. #1
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    Algebra

    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.
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  2. #2
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    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}
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