G is not simple
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G is not simple
Let \(\displaystyle{r:G\to GL_{n}(\mathbb{C})}\) be a group homomorphism. If there exists \(\displaystyle{g\in G}\)
such that \(\displaystyle{\rm{det}(r(g))=-1}\), then prove that \(\displaystyle{\left(G,\cdot\right)}\)
is not a simple group.
such that \(\displaystyle{\rm{det}(r(g))=-1}\), then prove that \(\displaystyle{\left(G,\cdot\right)}\)
is not a simple group.
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