G is not simple
Posted: Wed May 18, 2016 1:23 pm
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.