Does there exist a nontrivial subgroup \(G\) of \( GL(10, \mathbb{C}) \) such that each element in \(G\) is diagonalizable but the set of all the elements of \(G\) is not simultaneously diagonalizable?
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Does there exist a nontrivial subgroup \(G\) of \( GL(10, \mathbb{C}) \) such that each element in \(G\) is diagonalizable but the set of all the elements of \(G\) is not simultaneously diagonalizable?