Let $G$ be a finite subgroup of $GL_n(\mathbb{C})$. Prove that there exists a matrix $A\in GL_n(\mathbb{C})$ such that $AGA^{-1}\subseteq U_n(\mathbb{C})$.
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You may want to take a peek here: http://math.stackexchange.com/questions/176717/finite-subgroups-of-gln-mathbbc – DonAntonio Jan 08 '17 at 12:48
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see http://www.artofproblemsolving.com/community/c7h1365244_a_finite_subgroup_of_gl_nmathbbc – Gabriel Romon Jan 08 '17 at 13:03