G is not simple

Groups, Rings, Domains, Modules, etc, Galois theory
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Papapetros Vaggelis
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Joined: Mon Nov 09, 2015 1:52 pm

G is not simple

#1

Post by Papapetros Vaggelis »

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.
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